Question

A sinusoidal voltage of peak value $200\text{volt}$ is connected to a diode and resistor $R$ in the circuit shown so that half wave rectification occurs. If the forward resistance of the diode is negligible compared to $R$ then rms voltage (in volt) across $R$ is approximately -

• A. $200$
• B. $100$
• C. $\frac{200}{\sqrt{2}}$
• D. $280$

Answer 1

The correct option is B $100$


$V_{\text{avg.}}=\frac{\underset{0}{\overset{\pi }{\int }}200\sin \theta d\theta }{\underset{0}{\overset{2\pi }{\int }}d\theta }$
$=-\frac{200{\left[\cos \theta \right]}_0^{\pi }}{2\pi }$
$=\frac{200}{2\pi }$
Form factor of half wave rectifier $=1.57$
Form factor $=\frac{V_{\text{rms}}}{V_{\text{avg.}}}=1.57$
$V_{\text{rms}}=\frac{200}{\pi }\times 1.57$
$=\frac{200}{3.14}\times 1.57$
$=100$