An electric bulb is rated 220 V and 100 W. When it is operated at

Question

An electric bulb is rated

220 V

and

100 W .

When it is operated at

110 V,

the power consumed will be

Options:

A . 100 W

B . 75 W

C . 50 W

D . 25 W

Answer: Option D
:
D
Power consumed by the electric bulb,

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

, where

V

is the potential difference and

R

is the electrical resistance.
Given for 1st case:
Voltage

V_{1} = 220 V

and power consumed by bulb

P_{1} = 100 W,

In the 2nd case:
Voltage of the bulb,

V_{2} = 110 V

Power consumed by the bulb =

P_{2}

Since the resistance is the same as it is the same bulb

\frac{P_{1}}{P_{2}} = \frac{(V_{1})^{2}}{(V_{2})^{2}}

\frac{100}{P_{2}} = \frac{(220)^{2}}{(110)^{2}}

P_{2} = \frac{100 \times (110)^{2}}{(220)^{2}} = 25 W

Power consumed when the bulb is operated at 110V = 25W

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