Q61GATE 2001MCQ

AC-to-DC circulating current dual converters are operated with the following relationship between their triggering angles ( $\alpha _{1}\; and \; \alpha _{2}$ ).

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Q62GATE 2001MCQ

A half-wave thyristor converter supplies a purely inductive load, as shown in figure. If the triggering angle of the thyristor is $120^{\circ}$ , the extinction angle will be

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📖 Explanation

\begin{aligned} V_m \sin \omega t&=L\frac{di}{dt}\\ \frac{di}{dt}&=\frac{V_m}{L} \sin \omega t\\ \int_{0}^{i}di&=\frac{V_m}{L} \int_{\alpha }^{t}\sin \omega t\; dt\\ i&=\frac{V_m}{\omega L} \cos \omega t|_t^\alpha \\ i&=\frac{V_m}{\omega L} (\cos \alpha -\cos \omega t)\;\;...(i)\\ \text{For extinction angle, at }&\omega t=\beta ,i=0\\ \Rightarrow \;0&=\frac{V_m}{\omega L} (\cos \alpha -\cos \beta )\\ \text{Which gives, }& \cos \alpha = \cos \beta \\ \beta &=2 n \pi \pm \alpha \\ \text{For, } n&=1\\ \beta &=240^{\circ},480^{\circ} \end{aligned}