GATE 2024 IN – Question 33
The switch shown has been closed for a long time ($t<0$) and opens at $t=0$. The initial voltage derivative $dv_C/dt$ at $t=0^+$ is ______ V/s (nearest integer).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 15 to 15
Explanation
Before opening, the inductor is a DC short and the capacitor an open. The current is $12/(4+4)=1.5$ A and capacitor voltage 6 V. Inductor current is continuous. Immediately after the shunt resistor disconnects, all 1.5 A enters the capacitor: $dv_C/dt=i/C=1.5/0.1=\boxed{15}$ V/s.