Question

Electric power in terms of $V$ and $R$ is

• A. $V^2/R$
• B. $V/R^2$
• C. $R^2/V$
• D. $R/V^2$

Answer 1

The correct option is A

$V^2/R$

Step 1 - Formulas used

Electric power is the rate of doing work.

The formula for electric power $P$ is given by

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

Where $V$ is the applied voltage and $I$ is the current flowing through the circuit,

The expression for Ohm's law is given by

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

Where $R$ is the resistance.

Step 2 - Finding the formula for $I$

Rearrange equation $\left(2\right)$ to obtain the expression for $I$.

$I=\frac{V}{R}...\left(3\right)$

Step 3 - Finding the formula for power in terms of $V$ and $R$

Substitute $\frac{V}{R}$ for $I$ into equation $\left(1\right)$.

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

So, the formula for power is $P=\frac{V^2}{R}$.

Hence, option (a) is correct.