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GATE 2019 EE – Question 22

Electric Circuits · Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in AC circuits · 1 mark · Multiple choice

In the circuit shown below, the switch is closed at $t=0$. The value of $\theta$ in degrees which will give the maximum value of DC offset of the current at the time of switching is

Diagram for GATE 2019 EE question 22
  1. 60
  2. $-45$
  3. 90
  4. $-30$

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Correct answer: (B) $-45$

Explanation

The circuit has $R=3.77\ \Omega$ and $\omega L=377\times10\text{ mH}=3.77\ \Omega$, so the impedance angle is $\phi=45^\circ$. The DC offset is proportional to $\sin(\theta-\phi)$, which is largest in magnitude for $\theta-\phi=\pm90^\circ$, so $\theta=45^\circ-90^\circ=-45^\circ$.