GATE EC 2021 Set 1 — Question 57
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Network Theory → Transient & AC Analysis → RL, RC & RLC Transients
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Question
The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time .
Initially, when the switch is open, the capacitor is discharged and the ammeter reads zero ampere. After the switch is closed, the ammeter reading keeps fluctuating for some time till it settles to a final steady value. The maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is _________ A.
Correct answer
1.4 to 1.5
Solution
The ammeter measures the current through the inductor . The transfer function for the inductor current with respect to the source current is:Given , , and .
Natural frequency .
Damping ratio .
Since , the system is underdamped. The steady-state current is .
The maximum current is , where is the peak overshoot:Thus, .
Rounding to two decimal places, we get .
Natural frequency .
Damping ratio .
Since , the system is underdamped. The steady-state current is .
The maximum current is , where is the peak overshoot:Thus, .
Rounding to two decimal places, we get .
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