Ohm's Law: Difference between revisions

Latest revision as of 19:53, 5 December 2015

This page was created by Max Trussell, username: mtrussell6

Ohm's law is a very famous equation discovered by Georg Ohm describing the proportional relationship between voltage and current through some conductor. Most commonly this equation is seen in the form of

, with I representing current in amperes, V representing electric potential in volts, and R the resistance in ohms.

The Main Idea

Stripped down to its most basic, Ohm's Law exists so that either the electric potential, current, or total resistance of some conductor may be found when two out of the three are known quantities. This is possible because of the simple, linear relationship between the three.

A simple Ohmic circuit displaying I, V, and R as relevant to Ohm's Law. Source: reference 1

A Mathematical Model

While most often represented as [math]\displaystyle{ {I = \frac{|\Delta V|}{R}} }[/math], Ohm's Law may also be represented as [math]\displaystyle{ V = IR }[/math] or [math]\displaystyle{ {R = \frac{V}{I}} }[/math]. Noteworthy is the fact that Ohm's Law depends upon Ohmic resistance and near ideal conductors to be accurate. Fortunately, most simple circuits without capacitance or inductance fit this criteria as the wires offer minuscule resistance when compared to the various resistors in the circuit. Additionally at any given point in time, Ohm's Law applies to both alternating current and direct current. Also worth noting is that V does not necessarily represent the potential difference across a single source of electric potential (e.g. a battery) but rather the absolute value of the potential difference across an entire circuit.

A Computational Model

There are numerous programs to be found that simulate circuits via Ohm's Law, with many allowing for analysis beyond the standard scope of Ohm's Law. One such example is Phet's Circuit Construction Kit, a free, lightweight tool to create and analyze simple DC current circuits. Here is a video briefly describing its installation and use!

Examples

Simple

The most basic example of Ohm's Law in action involves a closed circuit with a single power source and a single Ohmic resistor.

Image Source: Max Trussell

For this example the power source will be 12 volts and the resistor will be 4 ohms. To solve for the current, simply plug in the given values to get [math]\displaystyle{ {\frac{12V}{4\Omega} = 3A} }[/math], meaning that the current is 3 amperes.

Middling

A slightly more complex example involves a closed circuit with a single power source and two Ohmic resistors in parallel.

Image Source: reference 2

In this case, R₁ is given to be 2 ohms, R₂ is given to be 4 ohms, and I is given to be 3 amperes. The first step is to remember that the R in the Ohm's Law equation represents total resistance, not individual resistors. In this case (Ohmic resistors in parallel), [math]\displaystyle{ {\frac{1}{R_{Net}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}} }[/math], plug in R₁ and R₂ to find [math]\displaystyle{ R_{Net} = \frac{4}{3} \Omega }[/math].

Now using the form of Ohm's Law [math]\displaystyle{ V = IR }[/math], plug in known values to get [math]\displaystyle{ (3A)(\frac{4}{3}\Omega) = 4V }[/math], so the electric potential across this circuit has been shown to be 4 volts.

Difficult

A more challenging application of Ohm's Law involves a closed circuit with two identical power sources connected in series to three resistors, two of which are in parallel.

Image Source: Max Trussell

Step 1: Find the Total Resistance

The total resistance for this circuit is going to equal the resistance of R₁ plus the resistance of R₂ and R₃ in parallel. Using the equation from the previous problem, [math]\displaystyle{ {\frac{1}{R_{P}} = \frac{1}{R_{2}} + \frac{1}{R_{3}}} }[/math], plug in R₂ and R₃ to get [math]\displaystyle{ R_{P} = 2.4\Omega }[/math]

Then for total resistance, R_P must be added to R₁ to get [math]\displaystyle{ 2.4\Omega + 2\Omega = 4.4\Omega }[/math]

Step 2: Find the Total Voltage

The total voltage for this circuit in this case is simply equal to the voltages of each power source added together, meaning [math]\displaystyle{ V_{T} = 2(4V) = 8V }[/math]

Step 3: Plug Into Appropriate Version of Ohm's Law

Now just plug the total resistance and voltage into [math]\displaystyle{ I = \frac{V}{R} }[/math] to get a current of 1.82 amperes

Connectedness

How is this topic connected to something that you are interested in?
Ohm's Law is the premise on which all simple circuits are created, meaning it is the foundation of nearly all modern electronics! Without Ohm's Law, there would be no cellphones, laptops, or even outlets in the wall.

How is it connected to your major?
As a computer scientist, in all likelihood I will not be directly using Ohm's Law for my work, but as stated previously, without it there would be no computers and thus, no computer science.

Is there an interesting industrial application?
Nearly all modern industry relies on electronics, from an assembly line to the lights in a small cafe. It is safe to say that without Ohm's Law, nearly every facet of modern industry would be dramatically different!

History

Back in 1827, German physicist Georg Ohm published his most recent work on resistance in electric circuits. In this work, entitled Die galvanische Kette, mathematisch bearbeitet, he first unveiled what is now know as Ohm's Law. Unfortunately due to political reasons, his work was never considered seriously until the 1840s and 1850s, at which point it became the leading theory on resistance in circuits, beating out rivals such as Barlow's Law. Ohm's work on both Ohm's Law and Ohmic resistors layed the foundations for contemporary circuitry and opened the gates to further scientific discoveries regarding the flow of electricity!

@@ Line 1: / Line 1: @@
+''This page was created by Max Trussell, username: mtrussell6''
-Template
+Ohm's law is a very famous equation discovered by Georg Ohm describing the proportional relationship between voltage and current through some conductor.  Most commonly this equation is seen in the form of
-Short Description of Topic
-Contents [hide]
+[[File:OhmsLaw.gif]], with I representing current in amperes, V representing electric potential in volts, and R the resistance in ohms.
-The Main Idea
-.1 A Mathematical Model
-.2 A Computational Model
-Examples
-.1 Simple
-.2 Middling
-.3 Difficult
-Connectedness
-History
-See also
-.1 Further reading
-.2 External links
-References
-The Main Idea[edit]
-State, in your own words, the main idea for this topic Electric Field of Capacitor
-A Mathematical Model[edit]
+==The Main Idea==
-What are the mathematical equations that allow us to model this topic. For example dp⃗ dtsystem=F⃗ net where p is the momentum of the system and F is the net force from the surroundings.
-A Computational Model[edit]
+Stripped down to its most basic, Ohm's Law exists so that either the electric potential, current, or total resistance of some conductor may be found when two out of the three are known quantities.  This is possible because of the simple, linear relationship between the three.
-How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
-Examples[edit]
+[[File:OhmicCircuit.gif|thumb|A simple Ohmic circuit displaying I, V, and R as relevant to Ohm's Law. Source: reference 1]]
-Be sure to show all steps in your solution and include diagrams whenever possible
-Simple[edit]
+===A Mathematical Model===
-Middling[edit]
-Difficult[edit]
-Connectedness[edit]
-How is this topic connected to something that you are interested in?
-How is it connected to your major?
-Is there an interesting industrial application?
-History[edit]
-Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
-See also[edit]
+While most often represented as <math>{I = \frac{|\Delta V|}{R}}</math>, Ohm's Law may also be represented as <math>V = IR</math> or <math>{R = \frac{V}{I}}</math>.  Noteworthy is the fact that Ohm's Law depends upon Ohmic resistance and near ideal conductors to be accurate.  Fortunately, most simple circuits without capacitance or inductance fit this criteria as the wires offer minuscule resistance when compared to the various resistors in the circuit.  Additionally at any given point in time, Ohm's Law applies to both [http://www.physicsbook.gatech.edu/AC alternating current] and direct current.  Also worth noting is that '''V''' does not necessarily represent the potential difference across a single source of electric potential (e.g. a battery) but rather the absolute value of the potential difference across an entire circuit.
-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[edit]
+===A Computational Model===
-Books, Articles or other print media on this topic
-External links[edit]
+There are numerous programs to be found that simulate circuits via Ohm's Law, with many allowing for analysis beyond the standard scope of Ohm's Law.  One such example is [https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc Phet's Circuit Construction Kit], a free, lightweight tool to create and analyze simple DC current circuits.  [https://www.youtube.com/watch?v=4ljzvLQG5tY Here] is a video briefly describing its installation and use!
-Internet resources on this topic
-References[edit]
+==Examples==
-This section contains the the references you used while writing this page
-Category: Which Category did you place this in?
+===Simple===
-Navigation menu
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+The most basic example of Ohm's Law in action involves a closed circuit with a single power source and a single Ohmic resistor.
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-Main page
+[[File:OhmsLawExample1.png]]
-Recent changes
+<br>''Image Source: Max Trussell''
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+For this example the power source will be 12 volts and the resistor will be 4 ohms.  To solve for the current, simply plug in the given values to get <math>{\frac{12V}{4\Omega} = 3A}</math>, meaning that the current is 3 amperes.
-Tools
+===Middling===
-What links here
-Related changes
+A slightly more complex example involves a closed circuit with a single power source and two Ohmic resistors in parallel.
-Upload file
-Special pages
+[[File:OhmsLawExample2.gif]]
-Printable version
+<br>''Image Source: reference 2''
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+In this case, R<sub>1</sub> is given to be 2 ohms, R<sub>2</sub> is given to be 4 ohms, and I is given to be 3 amperes.  The first step is to remember that the R in the Ohm's Law equation represents total resistance, not individual resistors.  In this case (Ohmic resistors in parallel), <math>{\frac{1}{R_{Net}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}}</math>, plug in R<sub>1</sub> and R<sub>2</sub> to find <math>R_{Net} = \frac{4}{3} \Omega</math>.
-This page was last modified on 1 November 2015, at 21:38.
-This page has been accessed 140 times.
+Now using the form of Ohm's Law <math>V = IR</math>, plug in known values to get <math>(3A)(\frac{4}{3}\Omega) = 4V</math>, so the electric potential across this circuit has been shown to be 4 volts.
-Privacy policyAbout Physics BookDisclaimersPowered by MediaWiki
+===Difficult===
+A more challenging application of Ohm's Law involves a closed circuit with two identical power sources connected in series to three resistors, two of which are in parallel.
+[[File:OhmsLawExample3.jpg|500px]]
+<br>''Image Source: Max Trussell''
+'''Step 1: Find the Total Resistance'''
+The total resistance for this circuit is going to equal the resistance of R<sub>1</sub> plus the resistance of R<sub>2</sub> and R<sub>3</sub> in parallel. Using the equation from the previous problem, <math>{\frac{1}{R_{P}} = \frac{1}{R_{2}} + \frac{1}{R_{3}}}</math>, plug in R<sub>2</sub> and R<sub>3</sub> to get <math>R_{P} = 2.4\Omega</math>
+Then for total resistance, R<sub>P</sub> must be added to R<sub>1</sub> to get <math>2.4\Omega + 2\Omega = 4.4\Omega</math>
+'''Step 2: Find the Total Voltage'''
+The total voltage for this circuit in this case is simply equal to the voltages of each power source added together, meaning <math>V_{T} = 2(4V) = 8V</math>
+'''Step 3: Plug Into Appropriate Version of Ohm's Law'''
+Now just plug the total resistance and voltage into <math>I = \frac{V}{R}</math> to get a current of 1.82 amperes
+==Connectedness==
+#How is this topic connected to something that you are interested in?<br>Ohm's Law is the premise on which all simple circuits are created, meaning it is the foundation of nearly all modern electronics!  Without Ohm's Law, there would be no cellphones, laptops, or even outlets in the wall.
+#How is it connected to your major?<br>As a computer scientist, in all likelihood I will not be directly using Ohm's Law for my work, but as stated previously, without it there would be no computers and thus, no computer science.
+#Is there an interesting industrial application?<br>Nearly all modern industry relies on electronics, from an assembly line to the lights in a small cafe. It is safe to say that without Ohm's Law, nearly every facet of modern industry would be dramatically different!
+==History==
+Back in 1827, German physicist Georg Ohm published his most recent work on resistance in electric circuits.  In this work, entitled ''Die galvanische Kette, mathematisch bearbeitet'', he first unveiled what is now know as Ohm's Law.  Unfortunately due to political reasons, his work was never considered seriously until the 1840s and 1850s, at which point it became the leading theory on resistance in circuits, beating out rivals such as Barlow's Law.  Ohm's work on both Ohm's Law and Ohmic resistors layed the foundations for contemporary circuitry and opened the gates to further scientific discoveries regarding the flow of electricity!
+== See also ==
+*[[Current]]
+*[[Loop Rule]]
+*[[Voltage]]
+===Further reading===
+*Matter and Interactions, 4th Edition, Chapters 18 and 19
+*Calculus Based Physics II by Jeffrey Shnick, free textbook--downloadable [http://www.anselm.edu/internet/physics/cbphysics/index.html here]
+===External links===
+*[http://www.physicsclassroom.com/class/circuits/Lesson-3/Ohm-s-Law Physics Classroom on Ohm's Law]
+*[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmlaw.html Hyper Physics on Ohm's Law]
+==References==
+#[http://faculty.plattsburgh.edu/donald.slish/figures/Basiccircuit.gif Basic Circuit. Digital image. Plattsburgh. N.p., n.d. Web]
+#[http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/paral1.gif Circuit With Parallel Resistors. Digital image. Cambridge University Department of Engineering and Biotechnology. N.p., n.d. Web.]
+#[http://www.physicsclassroom.com/class/circuits/Lesson-3/Ohm-s-Law "Ohm's Law." Ohm's Law. N.p., n.d. Web. 05 Dec. 2015.]
+#Chabay, Ruth W., and Bruce A. Sherwood. "Circuit Elements." Matter and Interactions, 4th Edition. N.p.: n.p., 2015. 783-99. Print.
+[[Category:Simple_Circuits]]