Single Choice

A steady potential difference of 100 V produces heat at a constant rate in a resistor. The alternating voltage which will produce half the heating effect in the same resister will be

A100 V
Correct Answer
B50 V
C70.7 V
D141.4 V

Solution

The power supplied to the resistor by DC source $$=\dfrac{V_{dc}^2}{R}$$
Energy given by AC source $$=\int_0^T \dfrac{V_0^2}{R}dt$$

Hence, $$\int_0^T \dfrac{V_0^2sin^2\omega t}{R}dt=\dfrac{1}{2}\times \dfrac{V_{dc}^2T}{R}$$

$$\implies V_0=V_{dc}=100V$$

SIMILAR QUESTIONS

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A light bulb is rated at $$100W$$ for a $$220V$$ ac supply. Calculate the resistance of the bulb.

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