Potential Difference

Potential difference — the energy transferred from electrical energy to other forms, per unit charge passing between two points:

V = W / Q

Measured in volts. One volt is one joule per coulomb.

Example: if 24 J is transferred when 3.0 C passes through a component, the p.d. across it is 24 ÷ 3.0 = 8.0 V. Read that as "8 joules transferred for every coulomb that passes".

Electromotive force (e.m.f.) — the energy transferred to electrical energy per unit charge, by a source such as a cell. Also measured in volts, and also energy per unit charge — the difference is the direction of the transfer.

The distinction that matters — e.m.f. describes a source putting energy into the circuit; potential difference describes a component taking energy out. A battery has an e.m.f.; a resistor has a p.d. across it. Calling the reading across a resistor an "e.m.f." is a genuine error, not a slip of vocabulary.

Why it is called a difference — potential is measured relative to a reference point, so only differences between two points have physical meaning. This is why a voltmeter has two leads and must be connected across something: asking for "the voltage at a point" is incomplete unless a reference is stated.

The electronvolt — a unit of energy, not of potential difference. One electronvolt is the energy transferred when an electron moves through a potential difference of one volt:

1 eV = 1.60 × 10⁻¹⁹ J

It is convenient in atomic and quantum physics, where joules would give inconveniently small numbers.

Example: converting is simply multiplying or dividing by the electronic charge. A photon of energy 3.5 eV carries 3.5 × 1.60 × 10⁻¹⁹ = 5.6 × 10⁻¹⁹ J. The usual mistake is to treat eV as a voltage; it is an energy.