8.1 Meaning of resistance

Resistance describes how strongly a component opposes current. It is defined by R = V/I, where V is the potential difference across the component and I is the current through it. The unit is the ohm, Ω. A component has resistance 1 Ω when a p.d. of 1 V produces a current of 1 A.

Resistance does not “use up” current. It affects how much current flows for a given p.d. and causes electrical energy to be transferred, often to internal energy. A high resistance gives a smaller current than a low resistance when both have the same p.d.

8.2 Ohm’s law

For an ohmic conductor at constant temperature, current is directly proportional to potential difference. The V–I ratio is constant, so the resistance does not change. A graph of current against voltage is a straight line through the origin.

The phrase “at constant temperature” is essential. If current heats a wire, its resistance may increase and the graph may no longer remain perfectly straight. Ohm’s law is a behaviour of certain conductors under specified conditions, not a universal rule for every component.

8.3 Measuring resistance

Connect an ammeter in series with the component and a voltmeter in parallel across it. Record V and I, then calculate R = V/I. To obtain a reliable value, take several pairs of readings by varying the supply or using a variable resistor, then check whether the ratio is constant.

Switch off between readings if heating is significant. Use appropriate meter ranges and read analogue scales at eye level. The component’s resistance should be found from simultaneous voltage and current readings because both may change when the circuit is adjusted.

8.4 Resistance of a wire and length

For a uniform wire of the same material and cross-sectional area at constant temperature, resistance is directly proportional to length. A longer wire gives electrons more opportunities to collide with the lattice, so the opposition to current is greater.

Doubling length approximately doubles resistance. This can be tested by connecting at different measured lengths of resistance wire while keeping current low enough to limit heating.

8.5 Resistance and cross-sectional area

For wires of equal material and length, a larger cross-sectional area gives a smaller resistance. A thick wire provides more parallel paths for charge flow. Resistance is inversely proportional to cross-sectional area for a uniform conductor.

Diameter must not be confused with area. Doubling diameter makes cross-sectional area four times larger, so resistance becomes about one quarter if all other factors remain constant.

8.6 Material and temperature

Different materials have different resistivities. Copper has low resistivity and is suitable for connecting wires, while nichrome has higher resistivity and withstands high temperatures, making it useful in heating elements.

For most metals, resistance increases with temperature because greater lattice vibration causes more frequent electron collisions. For thermistors and some semiconductors, resistance can decrease strongly as temperature rises because the number of mobile charge carriers increases.

8.7 Using graphs to determine resistance

On a graph of voltage V on the vertical axis against current I on the horizontal axis, gradient V/I equals resistance. On a graph of current I vertically against voltage V horizontally, gradient I/V equals conductance, so resistance is the reciprocal of the gradient.

Always inspect the axis labels before using a slope. Many incorrect answers come from assuming every straight-line graph has gradient equal to resistance.

Worked examples

Practical focus

Examination guidance

Check your understanding

1. A component has 12 V across it and carries 0.50 A. Find resistance.
2. Why may a metal wire cease to obey Ohm’s law at high current?
3. How does resistance change if wire length triples?