Ohm’s Law Explanation and Verification Brett MacDonald Andrew Misquita Michael Ramsay Dec.15/09

Agenda 1. Introduction 2. Principles of Ohm’s Law 3. Verifying Ohm’s Law 4. Summary

Introduction Background Purpose Methodology

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: 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 performed were not meant to make discoveries or find new concepts, they are simply used to prove and verify Ohm’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.

Any change to potential difference, current, or resistance has a direct and 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 a straight line.

Using point A on the diagram above, Ohm’s Law can be used to find resistance and verify the results. At this point, current is 8 Amps, and potential difference is 40 Volts. If Ohm’s law is rearranged to solve for resistance we should get a value of 5 Ohms. This simple calculation is proof of Ohm’s law, although it is important to take into consideration that this is a very basic example of the relationship.

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 to calculate 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]

Series Circuit 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 Voltage drop across R2 10.34V 10.23V -1.06% Voltage drop across R3 7.26V 7.34V 1.10%

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 0%

Analysis After completing the experiment it was found that the predicted values 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 that Ohm’s Law holds true for both parallel and series circuits. No further calculations 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 section Titled “Principles of Ohm’s Law”, the law was explained using the analogy that effect in a physical system is equal to the cause divided by its opposition. The effect would be the flow of charge, or current produced by the circuit. The cause would be the applied voltage, or potential difference introduced, and the opposition to that flow of charge would be the total resistance of the circuit.

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

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