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

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100 W

75 W

50 W

25 W

answer is D.

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Detailed Solution

When an electric bulb rated

220 V

and

100 W

is operated on

110 V

, the power consumed will be

25 W

.
It is known that “the power

(P)

of the electrical appliance is given by the result of the ratio of the square of the potential difference

(V)

to the resistance

(R)

offered.
It is given that potential difference

V = 220 V

and power

P = 100 W

.
Mathematically, the power can be written as

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

To know the resistance of the appliance the above relation can be written as

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

On substituting the given values, we get the resistance as

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

\Rightarrow R = 484 Ω

Therefore, the power consumed by the bulb at 110 V is

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

\Rightarrow P = \frac{110^{2}}{484}

\Rightarrow P = 25 W

Hence, the power consumed by the bulb is

25 W

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