Question

Derive the relationship between electrical energy and electric power.

Answer 1

Step 1 - Formulas

Consider that the applied voltage is $V$ and the current flowing through the circuit for time $t$ is $I$.

The formula for electrical power $P$ is

$P=V\times I...\left(1\right)$

The formula for electric energy $E$ is

$E=V\times I\times t...\left(2\right)$

Step 1 - Finding the relationship between electrical energy and electric power

Divide equation $\left(2\right)$ by equation $\left(1\right)$.

$$\begin{gathered} \frac{E}{P}=\frac{V\times I\times t}{V\times I} \\ \frac{E}{P}=t \\ E=P\times t \end{gathered}$$

Hence, the relationship between electrical energy and electric power is $E=P\times t$.