GATE EC 2019 Set 1 — Question 40
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Network Theory → Transient & AC Analysis → Sinusoidal Steady-State
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Question
In the circuit shown, if volts, and , then the steady-state current , in milliamperes (mA), is
Correct answer
(C) 3 sin(1000 t) + cos(1000 t)
Solution
Given rad/s, , and .
The capacitive reactance is .
In phasor domain, and (in k). The source voltage is .
The circuit consists of a bridge in parallel with a resistor . The bridge has branches , , , and .
Since and , the bridge is balanced. No current flows through the middle branch.
The bridge impedance is .
The admittance of the bridge is .
The bottom resistor is in parallel with the bridge, so .
Total admittance .
Total current phasor .
Converting back to time domain: .
The capacitive reactance is .
In phasor domain, and (in k). The source voltage is .
The circuit consists of a bridge in parallel with a resistor . The bridge has branches , , , and .
Since and , the bridge is balanced. No current flows through the middle branch.
The bridge impedance is .
The admittance of the bridge is .
The bottom resistor is in parallel with the bridge, so .
Total admittance .
Total current phasor .
Converting back to time domain: .
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