Potential Difference (Voltage)

In a circuit, charges move because there is a push between two points. This push is called potential difference (p.d.), or voltage. It tells you how much energy each coulomb of charge gains or loses between those points.

Definition and units

Potential difference is the work done (energy transferred) per unit charge between two points.

1 volt means 1 joule of energy is transferred per coulomb of charge.

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

Where $V$ is voltage in volts (V), $W$ is work/energy in joules (J), and $Q$ is charge in coulombs (C).

Analogy

Think of water flowing down a hill. The height difference gives water energy to flow. In circuits, potential difference is like the height difference: it gives electric charge energy to move through components.

p.d., e.m.f., and circuit rules

• e.m.f. is the p.d. supplied by a source (like a battery). It is the energy per charge given to the charges.
• Across components, p.d. shows energy per charge transferred to that component (for example, to heat a resistor or light a lamp).
• In series, p.d.s across components add up to the battery’s e.m.f.
• In parallel, the p.d. across each branch is the same as the p.d. across the supply.

Measuring p.d. with a voltmeter

• Connect the voltmeter in parallel across the two points or the component.
• Choose the correct range; start high and adjust down if needed.
• Match polarity for d.c.: red lead to the more positive side.
• A voltmeter has high resistance so it takes very little current.

Useful equations

• Energy and charge: $V = \frac{W}{Q}$.
• For a conductor obeying Ohm’s law: $V = IR$. At constant current, increasing resistance increases p.d.