question_answer

A sinusoidal voltage of peak value 200 volt is I 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, the rms value of voltage across R in volts is approximately.                          

A)  200                                       

B)  100

C)  \[100\sqrt{2}\]                                

D)  283

Correct Answer: B

Solution :

The wave form after half wave rectification is shown in figure The rms value of voltage is given by: \[\sqrt{V_{rms}^{2}}=\sqrt{\frac{1}{T}\int_{0}^{T}{{{V}^{2}}dt}}=\] \[=\sqrt{\frac{1}{T}\left[ \int_{0}^{T/2}{V_{0}^{2}}\sin \omega tdt+\int_{T/2}^{T}{0dt} \right]}\] \[=\frac{V_{0}^{2}}{4}\] \[{{V}_{rms}}=\frac{{{V}_{0}}}{2}=\frac{200}{2}=100\,\,W\]