# Potential difference

The potential difference or voltage (p.d. or $$V$$) between two points in a circuit is equal to the **energy that is lost** in moving a charge of one coulomb between two points in a circuit.

This energy loss is due to the **electrical resistance** of wires and circuit components (like resistors).

If there are no circuit components then **all** of the energy loss happens inside the wires. This causes the wires to become very hot!

The potential difference is measured in **volts $$(\text{V})$$** or joules per coulomb $$(\text{J }/ \text{ C})$$.

The **potential difference (or voltage)** $$V$$ can be expressed in terms of energy $$W$$ (sometimes $$E$$) and charge $$Q$$ using:$$$V=\frac{W}{Q}$$$ Recall that voltage is the work done per unit charge.

The symbol $$W$$ is used to refer to energy in formulae in the study of electricity and magnetism to avoid confusion because $$E$$ is also used to symbolise the e.m.f.

Voltage can also be expressed in terms of power $$P$$ and current $$I$$ by dividing the numerator and denominator of the formula above by time $$t$$: $$$\begin{align*} V&=\frac{W/t}{Q/t}\\ &=\frac{P}{I} \end{align*}$$$The potential difference can therefore also be defined as the power loss per unit current, or the rate of energy loss per unit current. All of these definitions are equivalent.

**Potential difference (p.d.)** and **electromotive force (e.m.f.) ** are closely related. Both are measured in volts.

The e.m.f. describes the **energy supplied** to a coulomb of charge in order to move it around the circuit.

The p.d. describes the **energy lost** between two points in a circuit (such as between the two ends of a resistor) by one coulomb of charge as it moves around the circuit.

Conservation of energy implies that: $$$\Tred{\text{total e.m.f. }} = \Tblue{\text{total p.d.}}$$$

If this were not the case, the charges in the circuit would gain or lose energy and the current would either increase or decrease.