Physics Book - User contributions [en]

Wavelength

2016-03-02T01:10:19Z

Okaykeeseok: /* Wavelength */

==Wavelength==

[[File:Wiki343333.jpg|right|800px]]In physics, wavelength is the distance in which wave's shape repeats. Wavelength is usually determined by measuring the distance between repeating patterns. Wavelength is commonly designated by the Greek letter, lambda (λ), and the SI unit of wavelength is nanometers(nm). Different length in wave cause different colors to be reflected. The concept can also be applied to periodic waves of non-sinusoidal shape. Sinusoidal shapes are the shapes of cosine and sine graphs. The term wavelength is also sometimes applied to modulated waves, which are the waves transmitted when information is conveyed. If a sinusoidal wave moving at a constant speed, wavelength is inversely proportional to frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. The formula for frequency and wavelength is v=fλ.

[[File:Wiki_00000.jpg|left|250px]]
Wavelength depends on the medium that a wave travels through, such as air, vacuum, and water. Wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves.

===A Mathematical Model===

We can easily determine wavelength for sinusoidal shaped graphs. For sin(θ), the wavelength would be 2π, since the wave repeats itself every 2π. For sine graph, the wavelength is determined by using the formula, 2π/x, where sin(xθ). [[File:Wiki_00006.jpg|right|300px]]

===A Computational Model===

In this case when we are observing the forces applied to a spring moving up and down, we can measure how force repeats by seeing the wavelength of the graph. [https://trinket.io/glowscript/23e96e1c2a]

==Examples==

===Simple===

Since frequency and wavelength are closely related, wavelength can be found if frequency is given. In the question below, λν = c. Since the speed of light and frequency is given, wavelength could be easily determined by plugging in the numbers.

[[File:Wiki_00007.jpg]]

===Middling===

A harmonic wave is traveling along a rope. The source generating the waves completes 50 to and fro motions in 25 s. A trough travels 2m in 4s. calculate the wavelength of the wave?

Solution:

Time taken for 50 oscillations = 25 s

Time for 1 oscillation, t = 25/50 = 0.5 s

Frequency of 1 oscillation, f = 1/0.5 = 2 Hz

The wave travels a distance of 2m in 4s. The wave speed is given by v = 2/4 = 0.5 ms-1

The wavelength is given by λ = v/f, λ=.5/2=.25

==Connectedness==
===How is this topic connected to something that you are interested in?===
This topic is not something what I am interested in, but I am willing to have interest from now on. While researching for wiki resource, I learned that different types are waves are deeply related to my current life. I would like to especially learn about the sound waves.
===How is it connected to your major===
I do not know how this will be connected to my major since I do not know anything about my major. Since concept of wavelength is used in diverse fields, I think this would be related to my major.
===Is there an interesting industrial application?===
There are interesting industrial application of waves. From radio to ultrasounds, waves are applied through industry.

==History==

[[File:neeewton.jpg|left|150px]]The concept of wavelength was first discovered by Isaac Newton. Many people were using prism to experiment with color before Newton’s famous experiments with light. When Newton was observing prism below sunlight, he saw different colors being emitted on the other side of the prism. Newton then realized that you need to move the screen far away in order to get a proper spectrum. After moving the screen and achieving a beautiful spectrum he conducted an experiment to prove that the prism was not colouring the light. He put a screen in the way of his spectrum, and this screen had a slit cut in it, and only let the green light go through. Newton built the first practical reflecting telescope and developed a theory of colour based on the observation that a prism decomposes white light into the many colours of the visible spectrum, and he also studied the speed of sound.

== See also ==

[http://physicsbook.gatech.edu/Color_Light_Wave| Color Light wave]

===External links===

[http://www.qrg.northwestern.edu/projects/vss/docs/communications/1-what-is-wavelength.html| Wavelength]

[http://www.physicsclassroom.com/class/sound/Lesson-1/Sound-is-a-Pressure-Wave| Sound Wave]

==References==

[http://www.juliantrubin.com/bigten/lightexperiments.html| Reference]

[http://formulas.tutorvista.com/physics/wavelength-formula.html| Reference 2]

[http://www.chemteam.info/Electrons/calc-wavelength-given-freq.html| Reference 3]

Wavelength

2016-03-02T01:10:09Z

Okaykeeseok: /* Wavelength */

==Wavelength==

[[File:Wiki343333.jpg|right|800px]]In physics, wavelength is the distance in which wave's shape repeats. Wavelength is usually determined by measuring the distance between repeating patterns. Wavelength is commonly designated by the Greek letter, lambda (λ), and the SI unit of wavelength is nanometers(nm). Different length in wave cause different colors to be reflected. The concept can also be applied to periodic waves of non-sinusoidal shape. Sinusoidal shapes are the shapes of cosine and sine graphs. The term wavelength is also sometimes applied to modulated waves, which are the waves transmitted when information is conveyed. If a sinusoidal wave moving at a constant speed, wavelength is inversely proportional to frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. The formula for frequency and wavelength is v=fλ.

[[File:Wiki_00000.jpg|left|250px]]
Wavelength depends on the medium that a wave travels through, such as air, vacuum, and water. Wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. hi

===A Mathematical Model===

We can easily determine wavelength for sinusoidal shaped graphs. For sin(θ), the wavelength would be 2π, since the wave repeats itself every 2π. For sine graph, the wavelength is determined by using the formula, 2π/x, where sin(xθ). [[File:Wiki_00006.jpg|right|300px]]

===A Computational Model===

In this case when we are observing the forces applied to a spring moving up and down, we can measure how force repeats by seeing the wavelength of the graph. [https://trinket.io/glowscript/23e96e1c2a]

==Examples==

===Simple===

Since frequency and wavelength are closely related, wavelength can be found if frequency is given. In the question below, λν = c. Since the speed of light and frequency is given, wavelength could be easily determined by plugging in the numbers.

[[File:Wiki_00007.jpg]]

===Middling===

A harmonic wave is traveling along a rope. The source generating the waves completes 50 to and fro motions in 25 s. A trough travels 2m in 4s. calculate the wavelength of the wave?

Solution:

Time taken for 50 oscillations = 25 s

Time for 1 oscillation, t = 25/50 = 0.5 s

Frequency of 1 oscillation, f = 1/0.5 = 2 Hz

The wave travels a distance of 2m in 4s. The wave speed is given by v = 2/4 = 0.5 ms-1

The wavelength is given by λ = v/f, λ=.5/2=.25

==Connectedness==
===How is this topic connected to something that you are interested in?===
This topic is not something what I am interested in, but I am willing to have interest from now on. While researching for wiki resource, I learned that different types are waves are deeply related to my current life. I would like to especially learn about the sound waves.
===How is it connected to your major===
I do not know how this will be connected to my major since I do not know anything about my major. Since concept of wavelength is used in diverse fields, I think this would be related to my major.
===Is there an interesting industrial application?===
There are interesting industrial application of waves. From radio to ultrasounds, waves are applied through industry.

==History==

[[File:neeewton.jpg|left|150px]]The concept of wavelength was first discovered by Isaac Newton. Many people were using prism to experiment with color before Newton’s famous experiments with light. When Newton was observing prism below sunlight, he saw different colors being emitted on the other side of the prism. Newton then realized that you need to move the screen far away in order to get a proper spectrum. After moving the screen and achieving a beautiful spectrum he conducted an experiment to prove that the prism was not colouring the light. He put a screen in the way of his spectrum, and this screen had a slit cut in it, and only let the green light go through. Newton built the first practical reflecting telescope and developed a theory of colour based on the observation that a prism decomposes white light into the many colours of the visible spectrum, and he also studied the speed of sound.

== See also ==

[http://physicsbook.gatech.edu/Color_Light_Wave| Color Light wave]

===External links===

[http://www.qrg.northwestern.edu/projects/vss/docs/communications/1-what-is-wavelength.html| Wavelength]

[http://www.physicsclassroom.com/class/sound/Lesson-1/Sound-is-a-Pressure-Wave| Sound Wave]

==References==

[http://www.juliantrubin.com/bigten/lightexperiments.html| Reference]

[http://formulas.tutorvista.com/physics/wavelength-formula.html| Reference 2]

[http://www.chemteam.info/Electrons/calc-wavelength-given-freq.html| Reference 3]

Fundamental Interactions

2016-03-02T01:09:50Z

Okaykeeseok:

Provide a brief summary of the page here

==Fundamental Interactions==

These are the most basic interactions in physical systems. There are four conventionally accepted fundamental interactions:
'''Gravitational, Electromagnetic, Strong force, and Weak force.'''

===Gravitational Interaction===

This is the ''Interaction'' that a planet or some other large body that has it's own gravitational field can exert on the System from the
Surroundings.
The '''Gravitational Interaction''' from the Earth on an object that is within Earth's gravitational field is 9.81 meters per second squared (m/s^2).

===Electromagnetic Interaction===

This is the ''Interaction'' that charged particles can exert on the System from the Surroundings.
Here we use '''Coulomb's Constant''' (8.98*10^9 n/m^2 (newtons*meters squared)) to describe the ''Interaction'' between electrically charged particles.

===Strong Force===

This is the ''Interaction'' between subatomic particles of matter. The strong force binds quarks together
in clusters to make more-familiar subatomic particles, such as protons and neutrons. It also holds together the atomic nucleus.

===Weak force===

This is the ''Interaction'' that governs the decay of unstable subatomic particles such as mesons.
It also initiates the nuclear fusion reaction that fuels the Sun.

==References==

Matter and Interactions 4th Edition

I can't submit this for grading on WebAssign yet, so I'll just leave my signature with timestamp here. --[[User:Austinrocket|Austinrocket]] ([[User talk:Austinrocket|talk]]) 17:38, 25 October 2015 (EDT)

Fundamental Interactions

2016-03-02T01:09:34Z

Okaykeeseok:

Provide a brief summary of the page here

==Fundamental Interactions==sadsad

These are the most basic interactions in physical systems. There are four conventionally accepted fundamental interactions:
'''Gravitational, Electromagnetic, Strong force, and Weak force.'''

===Gravitational Interaction===

This is the ''Interaction'' that a planet or some other large body that has it's own gravitational field can exert on the System from the
Surroundings.
The '''Gravitational Interaction''' from the Earth on an object that is within Earth's gravitational field is 9.81 meters per second squared (m/s^2).

===Electromagnetic Interaction===

This is the ''Interaction'' that charged particles can exert on the System from the Surroundings.
Here we use '''Coulomb's Constant''' (8.98*10^9 n/m^2 (newtons*meters squared)) to describe the ''Interaction'' between electrically charged particles.

===Strong Force===

This is the ''Interaction'' between subatomic particles of matter. The strong force binds quarks together
in clusters to make more-familiar subatomic particles, such as protons and neutrons. It also holds together the atomic nucleus.

===Weak force===

This is the ''Interaction'' that governs the decay of unstable subatomic particles such as mesons.
It also initiates the nuclear fusion reaction that fuels the Sun.

==References==

Matter and Interactions 4th Edition

I can't submit this for grading on WebAssign yet, so I'll just leave my signature with timestamp here. --[[User:Austinrocket|Austinrocket]] ([[User talk:Austinrocket|talk]]) 17:38, 25 October 2015 (EDT)

User:Okaykeeseok

2015-12-03T06:43:36Z

Okaykeeseok: Created page with "==The Main Idea== Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can..."

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 Ω</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 Ω </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 Ω </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 Ω </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

*[http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009 Circuits in real Life]

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===
Introduction to Electric Circuits 9th edition James A. Svoboda Richard C. Dorf

Basic Electric Circuit Theory Issaak D. Mayegoyz W.Lawson

Matter & Interactions Vol. II: Electric and Magnetic Interactions, 4th Edition R. Chabay B Sherwood

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

Including the 3 textbook, I have refereed to the following external sources to create a wikipage.

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

[[Category:Simple Circuits]]

Parallel Circuits

2015-12-03T06:39:42Z

Okaykeeseok: /* Solution */

Parallel Circuits

2015-12-03T06:39:21Z

Okaykeeseok: /* Solution */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 Ω</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 Ω </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

*[http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009 Circuits in real Life]

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===
Introduction to Electric Circuits 9th edition James A. Svoboda Richard C. Dorf

Basic Electric Circuit Theory Issaak D. Mayegoyz W.Lawson

Matter & Interactions Vol. II: Electric and Magnetic Interactions, 4th Edition R. Chabay B Sherwood

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

Including the 3 textbook, I have refereed to the following external sources to create a wikipage.

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

[[Category:Simple Circuits]]

Parallel Circuits

2015-12-03T06:39:04Z

Okaykeeseok: /* Middling */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 Ω</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

*[http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009 Circuits in real Life]

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===
Introduction to Electric Circuits 9th edition James A. Svoboda Richard C. Dorf

Basic Electric Circuit Theory Issaak D. Mayegoyz W.Lawson

Matter & Interactions Vol. II: Electric and Magnetic Interactions, 4th Edition R. Chabay B Sherwood

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

Including the 3 textbook, I have refereed to the following external sources to create a wikipage.

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

[[Category:Simple Circuits]]

Parallel Circuits

2015-12-03T06:38:40Z

Okaykeeseok: /* Middling */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 Ω</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 Ω, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

*[http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009 Circuits in real Life]

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===
Introduction to Electric Circuits 9th edition James A. Svoboda Richard C. Dorf

Basic Electric Circuit Theory Issaak D. Mayegoyz W.Lawson

Matter & Interactions Vol. II: Electric and Magnetic Interactions, 4th Edition R. Chabay B Sherwood

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

Including the 3 textbook, I have refereed to the following external sources to create a wikipage.

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

[[Category:Simple Circuits]]

Parallel Circuits

2015-12-03T06:38:13Z

Okaykeeseok: /* Solution */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 Ω</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

*[http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009 Circuits in real Life]

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===
Introduction to Electric Circuits 9th edition James A. Svoboda Richard C. Dorf

Basic Electric Circuit Theory Issaak D. Mayegoyz W.Lawson

Matter & Interactions Vol. II: Electric and Magnetic Interactions, 4th Edition R. Chabay B Sherwood

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

Including the 3 textbook, I have refereed to the following external sources to create a wikipage.

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

[[Category:Simple Circuits]]

Parallel Circuits

2015-12-03T06:35:05Z

Okaykeeseok: /* References */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

*[http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009 Circuits in real Life]

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===
Introduction to Electric Circuits 9th edition James A. Svoboda Richard C. Dorf

Basic Electric Circuit Theory Issaak D. Mayegoyz W.Lawson

Matter & Interactions Vol. II: Electric and Magnetic Interactions, 4th Edition R. Chabay B Sherwood

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

Including the 3 textbook, I have refereed to the following external sources to create a wikipage.

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

[[Category:Simple Circuits]]

Parallel Circuits

2015-12-03T06:31:52Z

Okaykeeseok: /* Connectedness */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

*[http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009 Circuits in real Life]

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===
Introduction to Electric Circuits 9th edition James A. Svoboda Richard C. Dorf

Basic Electric Circuit Theory Issaak D. Mayegoyz W.Lawson

Matter & Interactions Vol. II: Electric and Magnetic Interactions, 4th Edition R. Chabay B Sherwood

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:30:11Z

Okaykeeseok: /* Further reading */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===
Introduction to Electric Circuits 9th edition James A. Svoboda Richard C. Dorf

Basic Electric Circuit Theory Issaak D. Mayegoyz W.Lawson

Matter & Interactions Vol. II: Electric and Magnetic Interactions, 4th Edition R. Chabay B Sherwood

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:30:03Z

Okaykeeseok: /* Further reading */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===
Introduction to Electric Circuits 9th edition James A. Svoboda Richard C. Dorf
Basic Electric Circuit Theory Issaak D. Mayegoyz W.Lawson

Matter & Interactions Vol. II: Electric and Magnetic Interactions, 4th Edition R. Chabay B Sherwood

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:29:05Z

Okaykeeseok: /* Further reading */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===
Introduction to Electric Circuits 9th edition James A. Svoboda Richard C. Dorf
Basic Electric Circuit Theory Issaak D. Mayegoyz W.Lawson
Matter & Interactions Vol. II: Electric and Magnetic Interactions, 4th Edition R. Chabay B Sherwood

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:27:59Z

Okaykeeseok: /* Further reading */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===
Introduction to Electric Circuits 9th edition James A. Svoboda Richard C. Dorf
Basic Electric Circuit Theory Issaak D. Mayegoyz W.Lawson

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:26:08Z

Okaykeeseok: /* Further reading */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===
Introduction to Electric Circuits 9th edition James A. Svoboda Richard C. Dorf

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:25:35Z

Okaykeeseok: /* External links */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

*[http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-and-parallel-circuits/ All about parallel and series circuit]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:23:18Z

Okaykeeseok: /* External links */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===

===External links===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:23:09Z

Okaykeeseok: /* Further reading */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:22:19Z

Okaykeeseok: /* Further reading */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.regentsprep.org/regents/physics/phys03/bparcir/ Basics]
*[http://inventors.about.com/od/istartinventions/a/intergrated_circuit.htm Invention of Integrated Circuit]
*[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Circuit]

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:20:49Z

Okaykeeseok: /* Further reading */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===

*[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Parallel Resistor]
*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:16:14Z

Okaykeeseok: /* See also */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to help understand the concept of parallel circuit

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:15:39Z

Okaykeeseok: /* History */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robert Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to understand.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:14:25Z

Okaykeeseok: /* History */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name :[[Jack Kilby]], and :[[Robert Noyce]] in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to understand.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:13:42Z

Okaykeeseok: /* History */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robery Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to understand.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

File:Robertpp.jpeg

2015-12-03T06:13:03Z

Okaykeeseok:

File:Jackpp.jpeg

2015-12-03T06:11:19Z

Okaykeeseok: Jack Kilby

Jack Kilby

Parallel Circuits

2015-12-03T06:10:39Z

Okaykeeseok: /* History */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robery Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

[[File:jackpp.jpeg]]
[[File:robertpp.jpeg]]

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to understand.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:08:58Z

Okaykeeseok: /* History */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robery Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to understand.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:07:51Z

Okaykeeseok: /* History */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robery Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

[[File:historypp.jpeg]]

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to understand.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:04:50Z

Okaykeeseok: /* See also */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robery Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

:[[Node Rule]]
:[[Loop Rule]]
:[[Power in a circuit]]
:[[Current]]
:[[Ohm's Law]]

These pages would provide some basic information that we could refer to understand.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:03:21Z

Okaykeeseok: /* See also */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robery Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

:[[RC]]

When we thoroughly understand the general idea of a circuit, it's very useful to refer to more complicated circuit as RC cirucit.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T06:00:04Z

Okaykeeseok: /* See also */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robery Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.

:[[Series Circuit]]

First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Series Circuit

2015-12-03T05:59:30Z

Okaykeeseok: Created page with "claimed by Mchan46 ==Main Idea== :A Series Circuit is a simple type of electrical circuit in which components are placed in succession of one another. :The..."

claimed by [[User:Mchan46|Mchan46]]
==Main Idea==

:A Series Circuit is a simple type of electrical circuit in which components are placed in succession of one another.
:The electrical connection is not branched in any way. One can visualize this circuit as simply a closed loop.
:Often times, the simple series circuit may include but are not limited to: a number of resistors, switches, and of course, batteries.
:Keep in mind, if there is an open switch or break in the circuit, no current flows.

===A Mathematical Model===

:Kirchhoff's Current and Voltage Laws apply in a series circuit.
::Through Kirchhoff's Current Law, we know that the sum of all current going in must equal the sum of all current going out.
:::<math>\sum{I}_{in} - \sum{I}_{out} = 0</math>
::Since there are no nodes for the current to split up, the current throughout a series circuit will always be the same through each component.
::Through Kirchhoff's Voltage Law, the sum of all voltage in a closed system must be zero.
:::<math>\sum{V}_{Battery} - \sum{V}_{Components} = 0</math>
<br />
:Ohm's Law is extremely useful in finding the voltages, resistances, and current throughout the series circuit.
::Ohm's Law gives us the following formula:
:::<math>V=IR</math>; it can be rearranged to yield <math>I=\frac{V}{R}</math> and <math>R = \frac{V}{I}</math>
<br />
:Total Resistance in a series circuit is the sum of all resistances. It can be used to find the overall current in the circuit, which can then be used to find individual resistances.
::Total resistance is described by:
:::<math>R_T=\sum_{n=1}^N {R}_{Series}=R_1+R_2+R_3+...R_N</math>

===A Computational Model===

:The best way to visualize a series circuit is to draw a schematic, which is a simplified representation of the circuit in real life.
:Resistors are usually represented in a schematic with [[File:Resistor Symbol.png|100px]]
:Batteries are represented in a schematic by [[File:Schematic-symbols-battery.png|75px]]
:Switches can be open or closed. An open switch is represented by [[File:Schematic-symbols-switch.png|75px]]
==Examples==

For these examples, find the values specified.

===Simple===
Find the current in the circuit.
:[[File:Problem1Series_Circuits.JPG|350px]]

===Middling===
Find the voltage across the battery if the current in the circuit is 0.5 A
:[[File:Problem2Series_Circuits.JPG|350px]]

===Difficult===
The voltage across <math>R_1</math> is 5 volts. The voltage across <math>R_2</math> is 6 volts. What are the resistances of <math>R_1, R_2,</math> and <math>R_3</math> if the current measured across <math>R_3</math> is .65 A and the voltage of the battery is 16V?
:[[File:Problem3Series_Circuits.JPG|350px]]
==Solutions to Examples==
===Simple===
<math>I=0</math> Since the circuit is open, there is no way for current to flow through the circuit.

===Middling===
:1. Find Total Resistance
::<math>R_T=R_1+R_2+R_3=10+35+15=60</math> Ohms
:2. Use Ohm's Law (current is given already)
::<math>V=IR=0.5\bullet60=30</math> Volts

===Difficult===
:1. Note that current across a series circuit is the same.
::Current = 0.65 A
:2. Sum of battery voltage is equal to the sum of all voltage across resistors.
::<math>\sum{V}_{Battery} = \sum{V}_{Components}</math>
::<math>16 = 5 + 6 + V_3</math>
::<math>V_3 = 5</math>
:3. Use the rearranged Ohm's Law to find the resistances.
::<math>R=\frac{V}{I}</math>
::<math>R_1=\frac{5}{.65}=7.69</math> Ohms
::<math>R_2=\frac{6}{.65}=9.23</math> Ohms
::<math>R_3=\frac{5}{.65}=7.69</math> Ohms

==Connectedness==
:Series circuits are the most basic type of circuits.
:They are used in all electronics; even parallel circuits can be simplified into a series circuit!
:Some realistic applications include making lights, motors, and other electrical appliances work.

==History==

:Series circuits date as far back as when the first battery was invented.
:In the 1800's Alessandro Volta invented the first battery; it was originally used to produce hydrogen and oxygen from water.
:Around the 1880's, however, light bulbs were commercialized and used to illuminate cities- none of this could be done without the basic circuit.

== See also ==

:[[Ohm's Law]]
:[[Resistors and Conductivity]]
:[[Current]]
:[[Ammeters,Voltmeters,Ohmmeters]]
:[[Power in a circuit]]
:[[RL Circuit]]
:[[LC Circuit]]

===Further reading===

:Matter & Interactions, Vol. II: Electric and Magnetic Interactions, 4nd Edition by R. Chabay & B.Sherwood (John Wiley & Sons 2015)

===External links===

:[http://www.allaboutcircuits.com/ All About Circuits]
:[http://www.build-electronic-circuits.com/ BuildElectronicCircuits]
:[http://science.howstuffworks.com/environmental/energy/circuit3.htm History of Electrical Circuits]

==References==
:"All About Circuits - Electrical Engineering & Electronics Community." All About Circuits - Electrical Engineering & Electronics Community. Web. 30 Nov. 2015.
:"Build Electronic Circuits - Electronics Explained in a Simple Way." Build Electronic Circuits. Web. 30 Nov. 2015.
:Matter & Interactions, Vol. II: Electric and Magnetic Interactions, 4nd Edition by R. Chabay & B.Sherwood (John Wiley & Sons 2015)
:Soclof, Sidney. HowStuffWorks. HowStuffWorks.com. Web. 30 Nov. 2015.

[[Category:Simple Circuits]]

Parallel Circuits

2015-12-03T05:57:13Z

Okaykeeseok: /* See also */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robery Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

You could refer to other topics where you can build more idea about the circuits.
:[[Series Circuit]]
First, you should know clearly about the series circuit in order to understand the basic circuit design. In real life we could see a parallel circuit combined with the series circuit, as the example shown in before.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T05:53:48Z

Okaykeeseok: /* History */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robery Noyce in the mid 1950s. The work was not done in a corporation. They just came up with the same idea in the same time. Jack Kilby was working for Texas Instrument, whereas Robery Noyce was an research engineer who founded for Semiconductor Corporation. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with minimum cost. From the start of 1960s, many company started to use a chip, replacing the original transistors, and resistors. This integrated circuit is known as one of the most important invention in human kind.
I wanted to introduce this specific circuit, because this is what I'm really interested in in my area computer engineering. (Designing the core of the computer)

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T03:28:29Z

Okaykeeseok: /* History */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Integrated Circuit was invented by two inventors name Jack Kilby, and Robery Noyce in the mid 1950s. To design a complex computer machine, they needed something more small with more data, and information compared to original transistors, resistors, and capacitors. So they designed an integrated circuit that has many functions within a single chip. It was used to deal with complex matters with least space.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T03:23:03Z

Okaykeeseok: /* Connectedness */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer! In detail, I'm interested in the application of a simple circuit to design a computer. How integrated circuits are used to build a hardware and software.

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T03:15:45Z

Okaykeeseok: /* Connectedness */

==The Main Idea==

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance.
In a parallel circuit, the potential difference is identical with each resistor positioned in different branches.
If a single parallel circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

In order to understand the parallel circuit, it's critical to know the main difference between series circuit and parallel circuits.
In a series circuit the current is identical through out the circuit, whereas parallel circuit has current depending on the resistor running through the individual branch. Moreover, in a series circuit the voltage differs,whereas in parallel circuit the voltage is same everywhere.

===A Mathematical Model===

::<math>V=IR</math>
Using the basic Ohm's law we could determine the voltage, resistance, and current throughout a circuit.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N}</math>

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

'''More resistor in parallel circuit, less resistance.'''
So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

:::<math>V_{Total}=V_1=V_2=V_3...=V_N</math>

In a parallel circuit, potential difference through out the circuit is equal everywhere.

:::<math>I_{Total}=I_1+I_2+I_3+...I_N</math>

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[[File:Current.gif]]

:::<math>I_n=I_{Total}\frac{R_{Total}}{R_n}</math>

'''Current Divider Law'''
Since the current running through each branch of the circuit is dependent on the impedance of that branch, the current divider law can be used to determine the magnitude the current through each individual branch.

So if we want to find out the current in <math>R_1 </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}</math>

===A Computational Model===

[[File:ParallelCircuit.jpeg]]

This is a simple way to represent a Parallel Circuit. The schematic version is very useful when we want to compute the values, and understand the concept. <math>R </math> represents a resistor and the <math>Battery</math> represents the total <math>emf</math> in the circuit.

[[File:paralleldiagram.jpeg]]

This diagram is the actual Parallel Circuit we could see in real life. The actual battery could represent the total emf in the previous schematic sketch, and the light bulb would act as a resistor from the previous parallel circuit.

==Examples==

These are practical examples we could solve through the formula, and the concept we've learned through this Wiki Page.

===Simple===

'''Calculate the total resistance of this parallel circuit.'''

[[File:simplep.png]]

===Solution===

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} </math>

Using this formula we could derive the total resistance of a parallel circuit.

Plugging in 90 for <math>R_1 </math>, 45 for <math>R_2 </math>, and 180 for <math>R_3 </math>, we get

:::<math>{R}_{Total}=25.7143 ohm</math>

===Middling===

'''Calculate the current running through <math>R_1 </math>.'''

'''Total current running through the circuit is 5 ampere. <math>R_1 </math>= 4 ohm, and <math>R_2 </math>= 6 ohm'''

[[File:middlep.gif]]

===Solution===

In order to find out the current running through <math>R_1 </math>, we can use the current divider law.
First calculate the total resistance.

:::<math>\frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}</math>

Rearranging this formula we get

:::<math>{R}_{Total}=\frac{R_1R_2}{R_1+R_2}=2.4 ohm </math>

Now plug in all the value to the following equation.

:::<math>I_{Total}=5A </math>
:::<math>I_1=I_{Total}\frac{R_{Total}}{R_1}=3A</math>

===Difficult===
'''Calculate the current running through <math>R_2 </math>.'''

[[File:difficultpp.png]]

===Solution===

First we have to find out the total resistance of this circuit. Since we have both series and parallel component in the circuit, we have to add all the components to find out the total resistance.

:::<math>R_{Parallel}=\frac{R_2R_3}{R_2+R_3}=18.75 ohm </math>
:::<math>R_{Total}=R_1+R_{Parallel}+R_4=58.75 ohm </math>

Now using the Ohm's law we could determine the total current running through the circuit.

::<math>V_{Total}=I_{Total}R_{Total}</math>
::<math>V_{Total}=10V</math>
::<math>I_{Total}=\frac{V_{Total}}{R_{Total}}</math>
::<math>I_{Total}=0.17A</math>

We can now use the current divider law to calculate the current running through <math>R_2 </math>.

:::<math>I_2=I_{Total}\frac{R_{Parallel}}{R_2}=0.10625A</math>

To check our answer, calculate the current running through <math>R_3 </math>

:::<math>I_3=I_{Total}\frac{R_{Parallel}}{R_3}=0.06375A</math>

:::<math>I_{Total}=I_2+I_3=0.17A</math>

Since the total current in a parallel circuit equals to the sum of the current running through each branch, we could verify our answers.

==Connectedness==

Circuit, including parallel, series, RC, RL... , could be applied to many areas. Circuits are used for many the power sources in the world. In every day's life we encounter using electrical events from turning on lights, using a mp3 player, and so on. Majoring in electrical and computer engineering, I have to deal with many circuits, and apply it to the real world. I choose this topic to cover more details about the circuit, and since a lot of students had hard time solving the circuit problem in Test 3. I'm interested in this area, because I can really understand what I can't easily visualize it in real life. By studying circuit, I can understand how power or electricity works, and even computer!

http://scienceofeverydaylife.discoveryeducation.com/views/other.cfm?guidAssetId=D1507F6E-09C3-4E7B-B1E9-16708E402009

This website provides some very useful video that shows how simple circuits works in the real world.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Parallel Circuits

2015-12-03T03:12:04Z

Okaykeeseok: /* Connectedness */

Parallel Circuits

2015-12-03T03:10:51Z

Okaykeeseok: /* Connectedness */

Parallel Circuits

2015-12-03T02:53:07Z

Okaykeeseok: /* Solution */

Parallel Circuits

2015-12-03T02:51:33Z

Okaykeeseok: /* A Mathematical Model */

Parallel Circuits

2015-12-03T02:50:59Z

Okaykeeseok: /* The Main Idea */

Parallel Circuits

2015-12-03T02:50:16Z

Okaykeeseok: /* The Main Idea */

Parallel Circuits

2015-12-03T02:49:20Z

Okaykeeseok: /* Solution */

Parallel Circuits

2015-12-03T02:48:30Z

Okaykeeseok: /* Solution */

Parallel Circuits

2015-12-03T02:48:12Z

Okaykeeseok: /* Difficult */

Parallel Circuits

2015-12-03T02:47:45Z

Okaykeeseok: /* Solution */