Physics Book - User contributions [en]

Series Circuits

2017-04-10T02:50:21Z

Cwhiteman7: /* Main Idea */

claimed by Cameron Whiteman spring 2017
==Main Idea==

:A series circuit is the most simple type of electrical circuit in which components are placed in succession of one another. A circuit in series only has one loop that can be drawn throughout.
:The electrical connection is not branched in any way and any disruption of the circuit causes the entire circuit to lose current. One can visualize this circuit as simply a closed loop. simple
:circuits often contain multiple components of differing resistances and functions which can be solved for using the loop rule. These components include: resistors, switches, capacitors, inductors, and of course, batteries.

==The loop Rule==
:When attempting to solve a series circuit, the simple rule to follow is the Loop rule. This is derived from Kirchoff's laws as well as Ohm's law and allows for electric potential, current, or
:resistance(s) to be solved for. To begin, draw a loop beginning from the positive terminal of the battery and traveling in a mathematical loop on a path to the negative terminal. More
:difficult circuits may have multiple loops and require more calculation, however, in the end this rule should always be true. The sum of the current at each resistor multiplied
:by its resistance must be equal to the electric potential of the battery. In other words, sum of the current going into the circuit must be equal to sum of the current leaving.

===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>
 
: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>
 
: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>
 
:When solving circuits, the voltage across each component can be used in relation with Kirchhoff's Voltage Law in order to find unknown values.
::The voltage across an inductor is related by the following equation:
:::<math>\Delta V_{inductor} = L\frac{dI}{dt}</math>
::The voltage across a capacitor can be determined using the following formula:
:::<math> \Delta V_{capacitor} = \frac{Q}{C}</math>
::The voltage across a battery is found through the following equation:
:::<math> \Delta V_{battery} = Ɛ_{mf}</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]]
:In series, individual resistances can be added up throughought and the sum is equal to the entire resistance across the whole circuit.
:<math>R_\text{total} = R_1 + R_2 + R_n</math>

:Batteries are represented in a schematic by [[File:Schematic-symbols-battery.png|75px]]
:Batteries are what contain the electrochemical energy to power whatever you have connected to your circuit. In series, the total voltage
:of the system is equal to the sum of the voltages of the batteries connected, assuming that they are attached in the same direction
:(positive terminal to negative terminal). If not, then they cancel each other out and a "net voltage" can be determined.

:Switches can be open or closed. An open switch is represented by [[File:Schematic-symbols-switch.png|75px]]

:Inductors are represented in a schematic by [[File:Inductor symbol.svg|75px|]]
:The total inductance of a system is similar to that of resistors and is equal to the sum of the individual inductances across the circuit.

:Capacitors are represented by [[File:Capacitor Symbol.svg|40px|]]
:The following equation can be utilized to calculate the total capacitance of a system.
:<math>\frac{1}{C_\mathrm{total}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_n}</math>.

==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.
:The most commonly used example for a series circuit is in lighting. However, Series is generally not the
:ideal setup as the loss of one bulb causes the current to cease and loss of power to all bulbs. On a larger
:scale, the idea of series is used in everyday household appliances. The device, whether it be a lamp or toaster,
: is connected into the wall and a switch either flips on to connect the circuit, allowing current to flow or there is
: a disconnect in the system, causing the entire unit to fail.

:The most common usage of series circuits in physics appears when breaking down much more complex and detailed circuits
:that might even be in parallel. When doing this, Kirchoff's laws are utilized to break up the circuit into multiple individual loops
:that, at which point, can be treated as series circuits. This trick can be extremely useful for solving difficult circuits and allows even
: the most confusing problems to be broken down into the simplest form.

==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.
:Electric circuits involve both direct current, DC, and alternating current, AC. Direct current, when all of the current only flows in one direction, was first used by Thomas Edison for his electric power transmission. Alternating current, ;when the current alternates directions, was first discovered by Nikola Tesla while he was looking for a way to allow power transmissions to go longer distances than with DC.
:Gustav Robert Kirchoff was the main contributor to understanding how circuits worked. He was born March 12, 1824 and died on October 17, 1887. As a renowned German physicist,
:he proposed what are now universally accepted laws surrounding the way that circuits work as student in 1845.

== 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]]

2017-04-09T23:25:58Z

Cwhiteman7:

2017-04-09T21:45:17Z

Cwhiteman7:

Polarization of an Atom

2017-04-09T21:35:36Z

Cwhiteman7:

Claimed by Owen Fisher (ofisher3)

Edited by Aniruddha Nadkarni Fall 2016
CAMERON WHITEMAN 2017

This page serves to outline and explain the inner workings and hidden mechanisms of the polarization of an atom.

==The Main Idea==

In an atom, the cloud of electrons, while connected to the nucleus, is not exactly centered on the nucleus. For this reason, atoms can interact with external charges and become polarized. The nucleus and cloud of electrons can move relative to each other. If an external charge comes into the same space that an atom occupies or is close by, the charge creates an electric field, which exerts a force on the atom. "Applied" electric fields such as this explain why the electron cloud and nucleus can move relative to each other. For example, if a positive charge is placed to the left of an atom, an electric field will be created that shifts the electron cloud of the atom towards the positive charge (to the left) and will shift the net positive nucleus away from the charge (to the right) as two objects of the same charge repel each other. In this case, it is now more probable to find an electron to the left of the nucleus, rather than the right.
===A Mathematical Model===

<math>{\vec{F} = q\vec{E}}</math> where '''F''' is the force created by the electric field '''E''' and the charge of a particle '''q'''. This force is what causes the atom to become polarized.

<math>{\vec{p} = α\vec{E}}</math> for almost all materials, the dipole moment '''p''' of the polarized atoms or molecules is directly proportional to the magnitude of the applied electric field '''E'''. The constant '''α''' is called the "polarizability" of a particular material. Many of these polarizability values have been measured experimentally and can be found in reference volumes.

[[File:Figure_20_05_06(a)a.jpg]]

===A Computational Model===

[[File:u8l1e3.gif]]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Suppose that you have a negatively charged tape hanging from the desk, and you rub a wooden pencil on a wool sweater and bring it near the tape.
*If the tape swings toward the pencil, does this show that the pencil had been positively by rubbing it on the wool?
Not necessarily. Even if the pencil is uncharged, the charged tape will polarize the and be attracted by the induced dipoles.
*Can a charged object repel a neutral object? Why or why not?
Polarization always brings the unlike-sign charge closer, yielding a net attraction. Repulsion of an induced dipole can't happen. Therefore repulsion is the better test of whether an object is charged.

===Middling===
*Question Why are charged objects attracted to neutral objects?
The attraction of both positively and negatively charged invisible tape to your hand, and to many other neutral objects, is deeply mysterious. The net charge of a neutral object is zero, so your neutral hand should not make an electric field that could act on a charged tape, nor should your neutral hand experience a force due to the electric field made by a charged tape. Nothing in our statement of the properties of electric interactions allows us to explain this attraction!

A positive point charge with charge q acts on a an atom as shown below.

[[File:Example5.png]]

What is the electric dipole moment p of the atom?

<math>{\vec{p} = α\vec{E}}</math>

<math>E=\frac{1}{4 \pi \epsilon_0 } \frac{q}{r^2} \hat{r}</math>

<math>p=\frac{\alpha}{4 \pi \epsilon_0 } \frac{q}{r^2} \hat{r}</math>

What is the magnitude and direction of the electric force due to the induced electric field on the point charge? Assume the magnitude of the charge for either end of the dipole is q, and that r is much larger than s.

<math>{|{E_{dipole,axis}}|=\frac{1}{4 \pi \epsilon_0 } \frac{2q^2s}{r^3} \hat{r}</math>

The <math>q^2</math> in this equation comes from the fact that we multiply the Electric field by the charge it is acting on to get the electric force. The direction of this force will be in the negative x direction, since the negative end of the atom would be polarized closer to the positive point charge, and thus the force acting due to the electric field would also be in that direction.

===Difficult===
[[File:Difficult Question.JPG]]

==Connectedness==
How is this topic connected to something that you are interested in?
*Atoms are the composition of all life. Anything can be broken down into atoms and subatomic particles. If we are able to understand atoms we understand the fundamental concepts of all life, and that is pretty interesting in my opinion.

How is it connected to your major?
*Polarization of atoms is not directly related to my major of Mechanical Engineering; however, there are classes I am required to take such as Intro to Physics 2 and Chemistry where the polarization of atoms directly applies.

Is there an interesting industrial application?
*There are many interesting industrial applications of the polarization of atoms over a broad scope of fields.
*The polarization of atoms is what causes something known as van Der Waals forces, which are attractive forces between molecules or atoms that are weaker than traditional covalent or ionic bonds, but still play a fundamental role in the behavior of such particles. These forces are what allow creatures like spiders and geckos to scale walls, as the van Der Waals forces between small hairs for spiders and another adhesive material for geckos interact with the particles of the surface being scaled, and are strong enough to support the animal. Using technology that mimics this behavior, mechanical and materials engineering labs have created basic prototypes for tools that can allow humans to scale walls in the same fashion, which could be applied for construction work, rescue utility, and countless other applications.

Some of these include:

Chemistry
*Checking chirality of organic compounds
*Infrared spectroscopy
Astronomy
*Providing information on sources of radiation and scattering, polarization probes the interstellar magnetic field
*Polarization of cosmic microwave background is being used to study the physics of the early universe
3D Movies
*Images are projected from the projector with multiplexed polarization
*3D glasses with suitable polarized filters ensure that each eye receives only the intended image
Communication and Radar
*All radio transmitting and receiving antennas are intrinsically polarized-think FM and AM radio
*Vertical polarization is used to radiate a radio signal in all directions, such as those used in mobile phones
*Alternating vertical and horizontal polarization allows satellite communication systems to broadcast two separate transmissions on a single frequency
Material Science Engineering
*the relationship between strain and birefringence motivates the use of polarization in characterizing the distribution of stress and strain in prototypes
Navigation
*Sky polarization was used in the 1950s when navigating near the poles of the Earth's magnetic field when neither the sun nor stars were visible

==History==

The two scientists accredited with first coming up with the electron cloud model of the atom, on which atom polarization is based upon, are Ernest Rutherford, a New Zealand born British scientist, and Niels Bohr, a Danish physicist. Both of these gentlemen's atom models included the electron cloud. Rutherford released his model in 1911, and Bohr came out with his model shortly thereafter in 1913. Rutherford's model however, suggested that all atoms were unstable. Bohr corrected this by suggesting that the electrons in the atom could only have certain classical motions. Without these two men, we could never have discovered how the polarization of an atom works.

== See also ==

[[Polarization]]

===Further reading===

*''Polarization Functions for First and Second Row Atoms in Gaussian type MO-SCF Calculations'' by B. Roos and P. Siegbahn
*''General Contraction of Gaussian Atomic Orbitals: Core, Valence, Polarization, and Diffuse Basis Sets'' by Richard C. Raffenetti
*''Polarization Propagator Methods in Atomic and Molecular Calculations'' by Jens Oddershede, Poul Jørgensen, and Danny L. Yeager
*''Phase of the Atomic Polarization in High-Order Harmonic Generation'' by Maciej Lewenstein, Pascal Salières, and Anne L’Huillier

===External links===

http://www.physicsclassroom.com/class/estatics/Lesson-1/Polarization

http://academics.smcvt.edu/abrizard/EM/dielectric_I.pdf

http://budker.berkeley.edu/papers/pdfs/QBvisualisationPreprint.pdf

http://ocw.mit.edu/resources/res-6-001-electromagnetic-fields-and-energy-spring-2008/chapter-6/06.pdf

http://www.hho4free.com/electrical_polarization.htm

==References==

https://www.webassign.net/ebooks/mi4/toc.html?page=14.3

http://www.slideshare.net/pabitadhungel321/polarization-and-its-application

https://en.wikipedia.org/wiki/Bohr_model

[[Category:Fields]]