GATE 2023 EE – Question 55
The circuit shown in the figure has reached steady state with thyristor ‘T’ in OFF condition. Assume that the latching and holding currents of the thyristor are zero. The thyristor is turned ON at $t=0$ sec. The duration in microseconds for which the thyristor would conduct, before it turns off, is _____ (Round off to 2 decimal places).
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Correct answer: 7.29 to 7.37
Explanation
With T off the capacitor charges to 100 V. When T is triggered, the 4 Ω resistor carries a steady $100/4=25$ A through T, while the $C$–$L$ branch (in parallel with T) resonates: $\omega_0=\dfrac1{\sqrt{LC}}=0.5\times10^6$ rad/s and the branch current is $I_p\sin\omega_0t$ with $I_p=100\sqrt{C/L}=50$ A, flowing through T in the forward direction first. So $i_T=25+50\sin\omega_0t$ A. It falls to zero when $\sin\omega_0t=-0.5$, i.e. $\omega_0t=\pi+\pi/6=3.665$ rad, so $t=\dfrac{3.665}{0.5\times10^6}=7.33\ \mu$s.