Question

A steady P.D. of $10V$ produces heat at a rate of ${}^{\prime }{x}^{\prime }$ in a resistor. The peak value of A.C. voltage which will produce heat at the rate of $x/2$ in the same resistor is:

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

Answer 1

The correct option is C $10V$

Power $P=\frac{V_{rms}^2}{R}$
DC voltage :
So, $\frac{V_{rms}^2}{R}=X$
$\Rightarrow \frac{100}{R}=X$
$\Rightarrow R=\frac{100}{X}$
AC voltage :
Power $P=\frac{V_{rms}^2}{R}$
where $V_{rms}=\frac{V_{max}}{\sqrt{2}}$
$\frac{X}{2}=\frac{V_{max}^2}{2R}$
$\therefore$ $100=V_{max}^2$
$V_{max}=10V.$