Question

An SCR has maximum rms on state current of 70 A. If the SCR is used in the resistive circuit and the current waveform is half sine wave, then the value of average on state current rating of thyristor when conduction angle is ${60}^{\circ }$ will be

• A. 12.38 A
• B. 36.42 A
• C. 25.19 A
• D. 9.42 A

Answer 1

The correct option is C 25.19 A

$I_{avg}=\frac{1}{2\pi }{\int }_{{\theta }_1}^{\pi }{I}_m\sin \theta d\theta =\frac{I_m}{2\pi }(1+\cos {\theta }_1)$

$I_{rms}=\frac{I_m}{2\sqrt{\pi }}{(\pi -{\theta }_1+\frac{\sin 2\theta }{2})}^{1/2}$

$\text{For conduction angle},{\theta }_1={180}^{\circ }-{60}^{\circ }={120}^{\circ }$

$I_{avg}=\frac{I_m}{2\pi }(1+(-0.5\left)\right)=\frac{0.5}{2\pi }{I}_m=0.0795I_m$

$I_{rms}=\frac{I_m}{2\sqrt{\pi }}\left[(\pi -\frac{2\pi }{3}+\frac{\sin \frac{4\pi }{3}}{2})\right]=\frac{I_m}{2\sqrt{\pi }}{[\frac{\pi }{3}-\frac{0.8660}{2}]}^{1/2}$

$=\frac{I_m}{2\sqrt{\pi }}0.7837=0.221I_m$

$\therefore \text{Form factor}=\frac{I_{rms}}{I_{avg}}=\frac{0.221I_m}{0.0795I_m}=2.779$

$\therefore I_{avg}=\frac{70}{2.779}=25.1889=25.19A$