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GATE 2018 EE – Question 41

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 · 2 marks · Multiple choice

A DC voltage source is connected to a series L-C circuit by turning on the switch S at time $t=0$ as shown in the figure. Assume $i(0)=0$, $v(0)=0$. Which one of the following circular loci represents the plot of $i(t)$ versus $v(t)$?

Diagram for GATE 2018 EE question 41
  1. Locus (A)
  2. Locus (B)
  3. Locus (C)
  4. Locus (D)

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Show answer and explanation

Correct answer: (B) Locus (B)

Explanation

With $L=C=1$, $i(t)=5\sin t$ and $v(t)=5(1-\cos t)$. So $(v-5)^2+i^2=25$, a circle with centre $(5,0)$ and radius 5 that starts from the origin and is traversed with $i>0$ initially. That is locus (B).