Current, potential difference and resistanceAQA A-Level Physics: Revision notes

Electric current is the rate of flow of charge. For a constant current $I$, the charge $Q$ passing a point in time $t$ is

$I = \frac{Q}{t}$, or $Q = I t$

Current is measured in amperes (A). One ampere is one coulomb of charge per second. Charge is measured in coulombs (C).

Worked example: a current of 2.5 A flows for 3.0 minutes. $t = 180$ s, so $Q = 2.5 \times 180 = 450$ C.

The potential difference (pd) between two points is the work done (energy transferred) per unit charge passing between them:

$V = \frac{W}{Q}$, or $W = Q V$

The unit is the volt (V). A pd of 1 V means that 1 J of energy is transferred for each coulomb of charge. Across a battery, electrical energy is supplied to the charge; across a component such as a resistor, electrical energy is transferred to other forms such as thermal energy.

Worked example: a pd of 12 V across a motor while 30 C passes through it transfers $W = 30 \times 12 = 360$ J.

The resistance of a component is the pd across it divided by the current through it:

$R = \frac{V}{I}$

The unit is the ohm (Ω). One ohm is one volt per ampere. For a fixed pd, a larger resistance gives a smaller current.

This equation defines resistance for any component, even if the resistance changes with pd or current. At a given point, use the pd and current at that point.

Worked example: a pd of 6.0 V gives a current of 24 mA. $R = 6.0 / 0.024 = 250$ Ω.

These three definitions can be combined in multi-step problems:

1. Find the charge from $Q = I t$
2. Find the energy from $W = Q V$
3. Find the resistance from $R = V / I$

In a safety context, harm to a body depends on the current through it, which is $V / R$ for the pd across the body. A bird sitting on one bare cable has almost no pd between its feet, so almost no current flows through it, while a person touching a cable and the ground has a large pd across their body.