Question

The power dissipated in the transmission cables carrying current $I$ and voltage $V$ is inversely proportional to

• A. V
• B. $V^2$
• C. $\sqrt{V}$
• D. $\sqrt{I}$
• E. I

Answer 1

Answer: (B)

By power dissipated across a resistance
$P=V I $ or $I=\frac{P}{V}$
Loss in transmission $=I^{2} r$
$=\left(\frac{P}{V}\right)^{2} r$
$=\frac{P^{2}}{V^{2}} \cdot r \propto \frac{1}{V^{2}}$
So, loss in transmission is inversely proportional to $V^{2}$.