Question

A sinusoidal voltage of peak value $200\text{V}$ 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 $R$, the rms value of voltage across $R$ in volts is approximately

• A. $200$
• B. $100$
• C. $100\sqrt{2}$
• D. $283$

Answer 1

The correct option is B $100$


Wave output for a half wave rectifier circuit

For half wave rectifier circuit $V_{rms}^2=\frac{1}{T}{\int }_0^T{V}^{2}dt$
where, $V=V_{0}sin\omega t$
$V_{rms}^2=\frac{1}{T}[{\int }_0^{T/2}{V}_0^{2}si{n}^2\omega dt+{\int }_{T/2}^{T}0dt]$
$V_{rms}^2=\frac{1}{T}\left[{\int }_0^{T/2}{V}_0^{2}si{n}^2\omega dt\right]=V_{rms}^2=\frac{V_0^2}{4}\Rightarrow V_{rms}=\frac{V_0}{2}$
where, $V_{rms}=200V$
So, $V_{rms}=\frac{100}{2}=100V$