GATE EE 2023 Set 1 — Question 55
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Power Electronics → Power Semiconductor Devices → Thyristor Commutation
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Question
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 sec. The duration in microseconds for which the thyristor would conduct, before it turns off, is _____ (Round off to 2 decimal places).
Correct answer
7.1 to 7.5
Solution
Given the circuit parameters:
Supply voltage
Capacitance
Inductance
Resistance Initially, the thyristor is OFF and the circuit is in steady state. The capacitor is charged to the supply voltage, so .At , the thyristor is turned ON. The circuit becomes a series RLC circuit. The current is governed by the differential equation:Since , the equation simplifies to:The characteristic equation is .
Undamped natural frequency .
Damping ratio .Since , the circuit is underdamped. The damped natural frequency is:The current expression for an underdamped series RLC circuit with initial capacitor voltage is:where .The thyristor conducts as long as . It will turn off when the current first reaches zero after , which occurs at:Rounding off to two decimal places, the duration is . This falls within the accepted range of 7.1 to 7.5.
Supply voltage
Capacitance
Inductance
Resistance Initially, the thyristor is OFF and the circuit is in steady state. The capacitor is charged to the supply voltage, so .At , the thyristor is turned ON. The circuit becomes a series RLC circuit. The current is governed by the differential equation:Since , the equation simplifies to:The characteristic equation is .
Undamped natural frequency .
Damping ratio .Since , the circuit is underdamped. The damped natural frequency is:The current expression for an underdamped series RLC circuit with initial capacitor voltage is:where .The thyristor conducts as long as . It will turn off when the current first reaches zero after , which occurs at:Rounding off to two decimal places, the duration is . This falls within the accepted range of 7.1 to 7.5.
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