An electric bulb is rated $220\ V$ and $100\ W$. When it is operated on $110\ V$, the power consumed will be
$(a)$ 100 W
$(b)$ 75 W
$(c)$ 50 W
$(d)$ 25 W

The correct answer is $(d)$ 25 W.

Explanation:

Given: 

An electric bulb is rated $220\ V$ and $100\ W$. 

To do:

To calculate the power consumed by the electric bulb when it is operated on $110\ V$.

Solution:

Here, power consumed $P=100\ W$

Voltage $V=220\ V$

We know that $P=\frac{V^2}{R}$

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

Or $R=\frac{220^2}{100}$

Or $R=484\ \Omega$

When voltage is $110\ V$, then power consumed $P=\frac{V^2}{R}$

$=\frac{110^2}{484}$

$=\frac{12100}{484}$

$=25\ W$

Therefore, the power consumed is $25\ W$ when the bulb is operated on 110 V.

So, option $(d)$ is correct.