Physics 9702 · Paper 1

Potential Difference & E.m.f.

A volt is not a thing that flows. It tells you energy per coulomb: how many joules are transferred for each coulomb of charge.
A “12 V” battery means: the source supplies 12 J to each coulomb of charge as it moves round the circuit. Components then transfer that energy to other forms.

P.d. = energy per coulomb

The (p.d.) between two points is the energy transferred per unit charge as charge moves between them.

V = \frac{W}{Q}

Symbols

$V$ = potential difference (V)
$W$ = energy transferred (J)
$Q$ = charge that passes (C)

So 1 volt = 1 joule per coulomb. That is the definition of the volt.
Follow one coulomb round the circuit below. The battery gives it 12 J. It transfers 8 J in the first resistor and 4 J in the second. The joules always balance.

Follow one coulomb round the loop: the battery hands it 12 J, the 20 Ω resistor takes 8 J, the 10 Ω resistor takes 4 J. Every joule is accounted for.

Worked example

Energy from charge and p.d.

A lamp runs for 20 s with a current of 10 A, and 400 J of energy is transferred. Find the charge that flowed and the p.d. across the lamp.

Charge: $Q = It = 10 \times 20 = 200$ C.
P.d. is energy per coulomb: $V = \dfrac{W}{Q} = \dfrac{400}{200} = 2.0$ V.

Answer

Q = 200 \text{ C}, \quad V = 2.0 \text{ V}

P.d. or e.m.f.: energy supplied and transferred

Sources (cells, batteries, generators) supply energy to charges. The energy supplied per unit charge is called the of the source.
Components (resistors, lamps, motors) take energy from the charge. The energy taken per unit charge is the p.d. across the component.
Both are measured in volts, because both are joules per coulomb. The difference is the direction of the energy: e.m.f. is energy in, p.d. is energy out.
The name “electromotive force” is an old name. It is not a force. Just use the letters e.m.f.

	e.m.f.	p.d.
Where	across a source (cell, battery)	across a component (resistor, lamp)
Energy	given to the charge	taken from the charge
Definition	energy transferred by the source per unit charge	energy transferred to the component per unit charge

Same unit, opposite direction: e.m.f. is the energy each coulomb is given; p.d. is the energy each coulomb transfers away. Internal resistance, and what happens when a real battery cannot deliver its full e.m.f., comes in the D.C. circuits chapter.

Your turn— tap to reveal the worked answer (9702-style)

A battery of e.m.f. 9.0 V pushes 20 C of charge round a circuit. How much energy does the battery transfer?

Answer: $W = QV = 20 \times 9.0 = 180$ J. E.m.f. is joules per coulomb, so multiply by the coulombs. (9702-style)

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