Question

The relation between the current I flowing through a conducting material, the potential V between its ends and its resistance R is given by: $V=IR$. The relation between Power $P$ ,current I and resistance R can be given as $I=\sqrt{\frac{P}{R}}$ , which of the following is the correct relation between P in terms of V and R?

• A. $P=\frac{R}{V^2}$
• B. $P=\frac{V}{R}$
• C. $P=\frac{V^2}{R}$
• D. $P=V^2{R}^3$

Answer 1

The correct option is C $P=\frac{V^2}{R}$

Given $V=IR$ and $I=\sqrt{\frac{P}{R}}$

Then $V=IR$

Put the value $I$ in equation, we get

$V=\frac{P}{R}\times R$

Squaring both sides, we get

$\Rightarrow V^2=\frac{P}{R}\times R^2$

$\Rightarrow V^2=PR$

$\Rightarrow P=\frac{V^2}{R}$