Question

A sinusoidal voltage of rms value $220\, V$ is applied to a diode and a resistor $R$ in the circuit shown in figure, so that half wave rectification occurs. If the diode is ideal, what is the rms voltage across $R_1$ ?

• A. $55\sqrt{2} \,V$
• B. $110\,V$
• C. $110\sqrt{2}\, V$
• D. $220\sqrt{2} \,V$

Answer 1

Answer: (C)

Output rms vol.
$V_{\text {rms }}=\sqrt{\frac{1}{T} \int\limits_{0}^{T} V_{m}^{2} \cos ^{2} \cot }\, d t$
$=\sqrt{\frac{1}{T} \int\limits_{0}^{T /2} v_{m}^{2} \cos ^{2} \omega t \cdot d t+\frac{1}{T} \int\limits_{T / 2}^{T} 0 \cdot d t}$
$=\left(\frac{1}{2 \pi} \int\limits_{0}^{T} v_{m}^{2} \cos ^{2} \omega t \cdot d t\right)^{1 / 2} $
$\left(\cos ^{2} \theta=\frac{1-\omega \theta}{2}\right)$
$=\frac{220}{\sqrt{2}}$
$=110 \sqrt{2}\,v$