Question

A steady potential difference of $10V$ produces heat at a rate $x$ in a resistor. The peak value of the alternating voltage which will produce heat at a rate $\frac{x}{2}$ in the same resistor is

• A. $5V$
• B. $5\sqrt{2}V$
• C. $10V$
• D. $10\sqrt{2}V$

Answer 1

Answer: (C)

$10V$

Heat produced $\propto V^2$

Let $x=k\times V^{2}x=k\times 100k=x/100$

For A.C:

$x/2=k\times {V_1}^2{V_1}^2=\frac{x}{2k}{V_1}^2=50V_1=5\sqrt{2}$

It is the rms value peak value $=5\sqrt{2}\sqrt{2}=10V$