Ohm’s LawExplanation and Verification

Brett MacDonaldAndrew MisquitaMichael Ramsay

Dec.15/09

Agenda

1. Introduction2. Principles of Ohm’s Law3. Verifying Ohm’s Law4. Summary

• Background• Purpose• Methodology

Introduction

Background

• Ohm’s law was created in 1827 by Georg Ohm

• It is one of the most widely used and recognized laws

• Very important basis of all electronic and electrical systems

• Has remained unchanged for almost 200 years

Ohm’s Law deals primarily with the values of:

EIR

E IR ERI

V = Potential Difference (Volts)

I = Current (Amps)

R = Resistance (Ohms)

Ω = Universal symbol for Ohms

Common terms used:

Potential Difference (Volts) - Difference in charge (positive and negative) between two separated points.

Current (Amps) – The flow of charge in a circuit, per unit of time.

Resistance (Ohms) – A measure of the opposition to current flowing through a circuit.

Series Circuit – An electric current that passes through every component of a circuit without splitting up into separate sections

Parallel Circuit – An electric current that splits up due to several components that have a point in common.

Purpose

• Verify Ohm’s Law• Explain how it works• Demonstrate it in real circuits

Methodology

Sources Used:

• Books• Internet• Textbooks• Experimentation

Please note: The experiments performedwere not meant to make discoveries or find newconcepts, they are simply used to prove and verifyOhm’s Law

Principles of Ohm’s Law

• History of Georg Ohm• Explanation of Ohm’s law• Application in Industry

History of Georg Ohm

• Was born March 16, 1789 in Erlangen Germany

• Started career as a mathematics instructor

• Wrote an elementary book on geometry in 1812

• As a reward Georg was later sent to work at Jesuit Gymnasium of Cologne in 1817 to teach mathematics and physics

• Sophisticated equipment and instruments available to him in this school, allowed him to further his understanding of physical and mathematical principles

• His law first appeared in the book titled Die Galvanische Kette Mathematisch Bearbeite. (English translation: The Galvanic Circuit Investigated Mathematically)

• The book started with basic mathematics and then continued into his new theories of electrical properties.

• One of these properties was the proportionality of current, and voltage in a resistor, Ohm’s Law.

• He also adopted the unit of resistance, the Ohm.

Explanation of Ohm’s Law

When looking at physical systems, there is a basic concept that holds true for almost any situation involving a change.

Ohm's law is a great example of how this relationship works.

CauseEffectOpposition

CauseEffectOpposition

PotentialDifferenceCurrentResistance

Any change to potential difference, current, or resistance has a directand linear effect on the other two quantities.

Consider current plotted as a function of time, with a fixed resistance.As the voltage increases, the current should increase linearly and in astraight line.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

0

2

4

6

8

10

12

14

16

Current as a Function of Voltage with a Fixed Resistance (5 Ohms)

A

Using point A on the diagram above, Ohm’s Law can be used to findresistance and verify the results.

At this point, current is 8 Amps, and potential difference is 40 Volts. IfOhm’s law is rearranged to solve for resistance we should get a valueof 5 Ohms.

This simple calculation is proof of Ohm’s law, although it is important totake into consideration that this is a very basic example of therelationship.

EIR

ERI

408VoltsRAmps

5R Ω

Application

• Ohm’s law is used extensively in circuit analysis to find unknown quantities• Most commonly used in the work force by electrical and electronic

engineers• Used in the design process of any appliance consisting of electric

components

Some jobs that would require knowledge of Ohm’s Law:

• Car audio installation• Designing city power grids• Electronic repair jobs• Installation of home power supplies

[3]

Verification of Ohm’s Law

• Experimental Design• Predicted and Measured Values• Analysis

Experimental Design

In this experiment, 2 types of circuits were tested (Series and Parallel)

Series configuration:

Parallel Configuration:

In these experiments, Ohm’s Law will be used tocalculate the predicted values in each circuit.

For the series circuit it will be used to predict:

• Total current• Voltage drop across each resistor

For the parallel circuit it will be used to predict:

• Current across each parallel branch

[4]

Predicted Value

Measured Value

Percent Error (%)

R Total 9 kΩ 8.85 kΩ -1.67%

I Total 2.2mA 2.23mA 1.36%

Voltage drop across R1

2.2V 2.23V 1.36%

Voltage drop across R2

10.34V 10.23V -1.06%

Voltage drop across R3

7.26V 7.34V 1.10%

Series Circuit

Parallel Circuit

Predicted Value

Measured Value

Percent Error (%)

R total 660Ω 654Ω -0.91%

Current across R1 20mA 20.3mA 1.5%

Current across R2 4.26mA 4.34mA 1.88%

Current across R3 6.06mA 6.06mA 0%

Analysis

After completing the experiment it was found that the predictedvalues were extremely close to the measured values, not exceeding percent error of more than ±2%.

Due to the accuracy of these values, this experiment verifies thatOhm’s Law holds true for both parallel and series circuits. No furthercalculations or analysis is needed.

Possible Source of Error: fluctuating resistor values

Summary

The purpose of this presentation was to verify, explain,And demonstrate Ohm’s Law. In the first main sectionTitled “Principles of Ohm’s Law”, the law was explainedusing the analogy that effect in a physical system isequal to the cause divided by its opposition. The effectwould be the flow of charge, or current produced by thecircuit. The cause would be the applied voltage, orpotential difference introduced, and the opposition to thatflow of charge would be the total resistance of the circuit.

In the second section titled “Verification of Ohm’s Law” thelaw was verified using experimentation. The law wastested on both series and parallel circuits. Due to theVery minor discrepancy between the predicted andMeasured values, the final outcome of the experimentverified that Ohm’s Law holds true for both series andparallel circuits.

References

[1] Queensland Chamber of Agricultural Societies, “Images” 2009. [Online]. Available:http://www.qcas.net.au/images/Graphics%20GIF/33_books.gif. [Accessed Dec. 5/09].

[2] BDEG, “Goerg Ohm” 2005. [Online]. Available: http://bdeg.sopron.hu/~spider/Ohm.jpg. [Accessed Dec. 5/09].

[3] XJTAG, “Images” 2006. [Online]. Available: http://www.xjtag.com/images/press/30-03-06c.jpg. [Accessed Dec.7/09].

[4] modyoursystem, “Pics” 2007. [Online]. Available: http://www.modyoursystem.com/pics/multimeter.jpg. [AccessedDec. 12/09].

R. L. Boylestead, “Ohm’s Law, Power and Energy” in Introductory Circuit Analysis: eleventh edition, V. Anthony, R.Davidson, and L. Dimmick, Ed., Upper Saddle River, NJ: Pearson Prentice Hall, 2007, pp. 101-105..

Wikipedia, "Ohm's Law" 2009. [Online]. Available: http://en.wikipedia.org/wiki/Ohm's_law. [Accessed Nov.24, 2009].

Wikipedia, "Georg Simon Ohm" 2009. [Online]. Available: http://en.wikipedia.org/wiki/Georg_ohm.[Accessed Nov. 27, 2009].

Physics, "Ohm's Law" 2009. [Online]. Available:http://www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.intro.html. [Accessed Nov. 30, 2009].

All About Circuits, "How Voltage, Current, and Resistance Relate" 2009. [Online]. Available:http://www.allaboutcircuits.com/vol_1/chpt_2/1.html. [Accessed Dec. 1, 2009].