GATE EE 2022 Set 1 — Question 31
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Electric Circuits → Transient & AC Steady-State → Sinusoidal Steady-State
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Question
In the circuit shown below, the switch is closed at . The magnitude of the steady state voltage, in volts, across the resistor is _________. (round off to two decimal places).
Correct answer
4.95 to 5.05
Solution
At steady state (), the capacitor acts as an open circuit. Therefore, the branch containing the capacitor and the resistor carries no current.The circuit can be analyzed as two parallel branches connected across the source:
1.Branch 1: The capacitor in series with the resistor. At steady state, this branch is an open circuit.
2.Branch 2: A resistor in series with a parallel combination of a and a resistor.
To find the voltage across the resistor, we find the voltage across the parallel combination in Branch 2:- Equivalent resistance of the parallel part: .
- The voltage is determined by the voltage divider rule in Branch 2:
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