Question

The value of form factor in case of half wave rectifier is:

• A. $1.11$
• B. $1.57$
• C. $1.27$
• D. $0.48$

Answer 1

The correct option is B $1.57$

Form factor of half wave rectifier is $=\frac{I_{rms}}{I_{av}}.....\left(1\right)$

RMS value of current is

$I_{rms}=\sqrt{\frac{1}{2\pi }\underset{0}{\overset{\pi }{\int }}{i}^{2}d\theta }$

$=\sqrt{\frac{1}{2\pi }\underset{0}{\overset{\pi }{\int }}{I}_{max}^{\pi }{\sin }^2\theta d\theta }$

$=\frac{I_{max}}{\sqrt{2\pi }}\sqrt{\frac{1}{2\pi }\underset{0}{\overset{\pi }{\int }}{\sin }^2\theta d\theta }$

$=\frac{I_{max}}{\sqrt{4\pi }}{\sqrt{[\theta -\frac{1}{2}\sin 2\theta ]}}_0^{\pi }$

$=\frac{I_{max}}{\sqrt{4\pi }}\sqrt{\pi }$

$=\frac{I_{max}}{2}$

Average value of current,

$I_{av}=\frac{1}{2\pi }\underset{0}{\overset{\pi }{\int }}id\theta$

$=\frac{1}{2\pi }\underset{0}{\overset{\pi }{\int }}{I}_{max}\sin \theta d\theta$

$=\frac{I_{max}}{\pi }$

So, put above values in equations (1) and (2)

Form factor,

$=\frac{\frac{I_{max}}{2}}{\frac{I_{max}}{\pi }}$

$=\frac{\pi }{2}$

$=1.57$