Question

A sinusoidal voltage of rms value $220V$ 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. $110V$
• C. $110\sqrt{2}V$
• D. $220\sqrt{2}V$

Answer 1

Answer: (C)

Output rms vol.
$V_{\text{rms }}=\sqrt{\frac{1}{T}\underset{0}{\overset{T}{\int }}{V}_m^2{\cos }^2\cot }dt$
$=\sqrt{\frac{1}{T}\underset{0}{\overset{T/2}{\int }}{v}_m^2{\cos }^2\omega t\cdot dt+\frac{1}{T}\underset{T/2}{\overset{T}{\int }}0\cdot dt}$
$={\left(\frac{1}{2\pi }\underset{0}{\overset{T}{\int }}{v}_m^2{\cos }^2\omega t\cdot dt\right)}^{1/2}$
$\left({\cos }^2\theta =\frac{1-\omega \theta }{2}\right)$
$=\frac{220}{\sqrt{2}}$
$=110\sqrt{2}v$