Question

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

• A. 100 V
• B. 50 V
• C. 70.7 V
• D. 141.4 V

Answer 1

Answer: (A)

100 V

The power supplied to the resistor by DC source $=\frac{V_{dc}^2}{R}$

Energy given by AC source $={\int }_0^T\frac{V_0^2}{R}dt$

Hence, ${\int }_0^T\frac{V_0^{2}si{n}^2\omega t}{R}dt=\frac{1}{2}\times \frac{V_{dc}^{2}T}{R}$

$⟹V_0=V_{dc}=100V$