Electrical Energy Equation

Energy transferred by moving charge

When charge flows through an electrical component, energy is transferred by electrical work. In a resistor, for example, this increases its temperature. The amount of energy transferred depends on both the amount of charge that passes through and the potential difference across the component.

Charge, represented by $Q$, is measured in coulombs (C). It is different from current: charge tells us how much passes through, whereas current tells us how quickly charge flows.

Potential difference means energy per coulomb

Potential difference is the energy transferred per coulomb of charge between two points. It is measured in volts (V). A potential difference of 12 V across a lamp means that each coulomb passing through transfers 12 J of energy to the lamp.

To find the total energy transferred, multiply the amount of charge by the energy transferred per coulomb:

$$E = QV$$

Here, $E$ is energy transferred in joules (J), $Q$ is charge in coulombs (C) and $V$ is potential difference in volts (V).

At a fixed potential difference, doubling the charge doubles the energy transferred. For the same amount of charge, doubling the potential difference also doubles the energy transferred.

Applying and rearranging the equation

Choose the equation according to the quantity you need. If charge and potential difference are known, multiply them to find energy. If energy is known instead, rearrange by dividing:

$$Q = \frac{E}{V} \qquad V = \frac{E}{Q}$$

For example, a lamp transfers 66 J of energy when 5.5 C of charge passes through it. Its potential difference is:

$$V = \frac{66}{5.5} = 12\text{ V}$$

This result means that the lamp transfers 12 J for every coulomb passing through it. Multiplying the charge by this potential difference gives the total energy again: $5.5 \times 12 = 66\text{ J}$. The multiplication and division describe the same relationship from different directions.

Electrical energy equation

$$E = QV$$

• $E$: energy transferred, joules (J)
• $Q$: charge, coulombs (C)
• $V$: potential difference, (V)