GATE EE 2018 Set 1 — Question 41
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Electric Circuits → Transient & AC Steady-State → Second-Order RLC
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Question
A DC voltage source is connected to a series L-C circuit by turning on the switch S at time as shown in the figure. Assume . Which one of the following circular loci represents the plot of versus ?
Correct answer
(B) [figure]
Solution
For the given series LC circuit with a DC step input :
.
1.The voltage across the capacitor satisfies the differential equation: .
2.Since , we have .
3.Given , the equation becomes .
4.With initial conditions and , the solution is .
5.The current is .
6.Squaring and adding terms to eliminate :
.
7.This is the equation of a circle in the plane centered at with radius 5. This corresponds to option (B).
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