Question

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

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Answer 1

Answer:

• 25 W

Explanation:

The energy consumed by the appliance is given by the expression

↪P = VI = V²/R

The resistance of the light bulb can be calculated as follows:

↪R = V²/P

Substituting the values, we get

↪R = (220)²/100 = 484 Ω

Even if the supply voltage is reduced, the resistance remains the same. Hence, the power consumed can be calculated as follows:

↪P = V²/R

Substituting the value, we get

↪P = (110)²V/484 Ω = 25 W

Therefore, the power consumed when the electric bulb operates at 110 V is 25 W.

Answer 2

$\sf\green{Answer:}$

$P =\dfrac{V^2}{R}\\ \\ R = \dfrac{V^2}{P} \\ \\ \sf R=\dfrac {220\times220}{100}\\ \\ \sf 484Ω \\ \\ \sf The ~current ~flow~ in ~the ~circuit, I = \dfrac{V'}{R} ~(V ′ = supplied~ voltage) \\ \\ I =\dfrac{110}{484} = 0.2272A\\ \\ \sf The ~voltage~ drop ~across ~the ~bulb ~is ~110V \\ \\ \sf The ~power ~consumed ~by ~the ~bulb,</p><p>\\ \\ P_b\frac {V^2}{R} = \frac {110\times 110}{484} \\ \\ \sf P_b= 25 w$

$\sf\red{Therefore,~option~D~is~correct}$