GATE EE 2023 Set 1 — Question 29
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Electric Circuits → Network Elements & Sources → Initial Conditions in R, L, C
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Question
The value of parameters of the circuit shown in the figure are
For time , the circuit is at steady state with the switch ‘K’ in closed condition. If the switch is opened at , the value of the voltage across the inductor () at in Volts is ____________ (Round off to 1 decimal place).
For time , the circuit is at steady state with the switch ‘K’ in closed condition. If the switch is opened at , the value of the voltage across the inductor () at in Volts is ____________ (Round off to 1 decimal place).
Correct answer
7.9 to 8.1
Solution
1.Steady state for (K closed):
The inductor acts as a short circuit and the capacitor as an open circuit.The 10A current source sees two parallel branches: and .
Equivalent resistance .
Voltage across the parallel combination .
Current through inductor .
Voltage across capacitor .
2.At (K opened):
Inductor current and capacitor voltage cannot change instantaneously:.
.
KCL at the top node: .
The voltage at the top node can be calculated from the capacitor branch:
.
Now, for the inductor branch:
.
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