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)

$V^2$

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