Question

An electric bulb is rated 220V and 100W. When it is operated on 110V, the power consumed will be :

• A. 100W
• B. 75W
• C. 50W
• D. 25W

Answer 1

The correct option is D 25W

$\text{Step 1: Finding Resistance of bulb using given Ratings}$

Rating of bulb $P=100W,$ $V=220V$

Power, $P=\frac{V^2}{R}$

$\Rightarrow R=\frac{V^2}{P}$ $=\frac{220\times 220}{100}=484\Omega$

$\text{Step 2: Power consumed by bulb}$

Now the voltage drop across the bulb is $V^{\prime }=110V$

So, power consumed by the bulb will be:

$P_b=\frac{V^{\prime 2}}{R}=\frac{110\times 110}{484}$ $\text{(Resistance of bulb will remain same)}$

$P_b=25W$

The correct option is D.