A lamp of 100 W at 200 V is supplied current at 100 volts. It will be equivalent to the lamp of
A
50 W
B
40 W
C
25 W
D
10 W

Question

A lamp of 100 W at 200 V is supplied current at 100 volts. It will be equivalent to the lamp of

Examoogle · Accepted Answer

25 W

Explanation: Given: Rated power of lamp P1 = 100 W, Rated voltage V1 = 200 V, Applied voltage V2 = 100 V.

Formula Used: $$R = \frac{V^2}{P}, P_{new} = \frac{V_2^2}{R}$$

Steps: Calculate lamp resistance: The resistance of the lamp is constant and determined by its rated power and voltage: $R = \frac{V_1^2}{P_1}$.. Calculate new power: When the lamp is supplied with a different voltage $V_2 = 100 \,V$, the new power $P_2$ dissipated by the resistance $R$ is $P_2 = \frac{V_2^2}{R}$.. Final calculation: Perform the final division to find the power value.

Answer: C is correct because the power consumed is proportional to the square of the voltage, so reducing voltage to half reduces power to one-fourth ($100 \,W 	imes (1/2)^2 = 25 \,W$).

Exam Tip: In competitive exams, remember that for any resistor, $P \propto V^2$; if voltage is halved, power becomes $1/4$, and if voltage is doubled, power becomes $4$ times.

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