Core Unit III: Electricity
B. Current and Potential Difference

3. Ohm's Law

Key Concepts

Increased resistance in a circuit decreases conductance. Resistance and conductance are inversely related.

As the potential difference is increased across a given material in a circuit, the current flow through the material also increases. A graph of potential difference versus current for a given material illustrates this. (This does not apply to all materials.)

The potential difference between any two points in a conductor is directly proportional to the current flowing through it. (Ohm's Law. This only holds true for an ohmic material. Nonohmic materials do not display a direct relationship.)

   (Ohm's Law)

R is the resistance, measured in ohms.
1 ohm = 1 volt/ampere

The symbol used for the ohm is the Greek letter omega

The resistance of a cylindrical resistor depends on its length, its cross-sectional area, its temperature, and the resistivity of the material.

Resistance is directly proportional to the length (L) of the conductor. Resistance varies inversely with the cross-sectional area (A).

Resistance usually increases with temperature. Some materials exhibit superconductivity (i.e., resistance drops to zero) at lower temperatures. (Materials become superconductive at different temperatures.)

Resistance depends on the resistivity of the material. The resistivity is defined as the resistance of a cylinder of the material 1 metre long with a cross-sectional area of 1 m². Resistivity varies with temperature. It is measured in m²/m. (Some texts use m.)

Learning Outcomes

1. Define the following terms: resistance, conductance, superconductivity, resistivity.

2. Recognize that a relationship exists between the potential difference and the current in an electric circuit.

3. State Ohm's Law .

4. Apply Ohm's Law to problems in electricity.

5. Use the correct units and symbol for resistance.

6. Identify four factors which influence the resistance of a cylindrical resistor.

7. Express the proportionality statements for each factor which influences the resistance of a cylindrical resistor.

8. Express the correct units for the resistivity of a material.

9. Solve problems relating to the factors which influence the resistance of a cylindrical resistor.

Teaching Suggestions, Activities and Demonstrations

1. Investigate Ohm's Law experimentally. Develop a graph to illustrate the relationship between the potential difference and the current in a circuit.

2. Connect a thermistor to a voltmeter, a multirange ammeter, and a D.C. power supply. Place the thermistor in ice cold water. Slowly heat the water and record the electric meter readings at different temperatures until the boiling point of water is reached. Determine the resistance at different temperatures. Plot resistance as a function of absolute temperature and analyze the results to determine if a single temperature coefficient of resistance exists.

   For a long-term challenge project, place the thermistor in air drafts and note the effect. Develop a way of measuring wind velocity and relative humidity, and record the results. Search for any relationships that might emerge from the data.