Resistance and Ohm's Law

Resistance — a measure of how much a component opposes the flow of current:

R = V / I

with resistance in ohms (Ω), p.d. in volts and current in amperes. Rearranged, V = I R, which is the form most questions want.

Ohm's law — the current through a conductor is directly proportional to the p.d. across it, provided the temperature stays constant. That last clause is the whole point of the law, and dropping it is what turns a correct statement into a wrong one.

Ohmic conductor — a component that obeys Ohm's law, giving a straight line through the origin on a current–voltage graph. A fixed resistor and a length of wire at constant temperature are ohmic.

What affects the resistance of a wire:

• Length — resistance is proportional to length. Double the wire, double the resistance.
• Cross-sectional area — resistance is inversely proportional to area. A thicker wire has a lower resistance.
• Material — copper has a much lower resistance than nichrome of the same dimensions.
• Temperature — for a metal, resistance rises as temperature rises.

Why resistance rises with temperature in a metal. The metal ions vibrate more violently when hot, so the drifting electrons collide with them more often and lose energy more readily. More collisions means more opposition to flow.

Measuring resistance — set up the component in series with an ammeter and a variable resistor, with a voltmeter in parallel across it. Vary the current, record pairs of V and I, and plot V against I. A straight line through the origin confirms an ohmic conductor, and its gradient is the resistance.

Example: a 12 V supply drives 0.40 A through a resistor. Its resistance is R = V/I = 12 ÷ 0.40 = 30 Ω. If the resistor warms up and its resistance rises to 40 Ω, the same supply now drives only 0.30 A.

Resistance is not a fixed property of a component unless it is ohmic and at a steady temperature. A filament lamp has a different resistance at every brightness.