Question

Show that 'electric power is given by $\frac{V^2}{R}$. What is the SI unit of electric power?

Answer 1

Step 1: Electrical Energy:

The electrical power of the device is measured by the product of the voltage across the device and the current passing through it.

The electrical power is given by,

$P=VI$ ……(1)

Here, $P$ is the power, $V$ is the voltage and $I$ is the current.

According to ohm's law,

$V=IR$

Here, $R$ is the resistance that opposes the flow of the current.

Step 2: Derive the expression for current from the ohm's law equation,

$I=\frac{V}{R}$

Substitute the current expression in the equation (1),

$$\begin{gathered} P=V\times \frac{V}{R} \\ P=\frac{V^2}{R} \end{gathered}$$

Hence, the electrical energy is given by $\frac{V^2}{R}$.

Step 3: SI unit of electric power,

The electrical power is measured in watts. Therefore, the SI unit of the electrical power is the watt.