GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 62 of 65

Marks: +1, -0

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)

Solution:

i=V_{S} √{\;{C}/{L}} \sin ω t

where,

ω=\;{1}/{√{L C}}

So,

i=5 \sin t

i=C \;{d V}/{d t}

v=\;{1}/{C} ∫↙{0}↖{t} i d t=∫↙{0}↖{t} 5 \sin t d t=5(1-\cos t)

i=5 \sin t \;\;

and

\;\; v=5-5 \cos t ⇒(5-v)=5 \cos t

Squaring and adding

(5-v)^{2}+i^{2}=25

Or,

(v-5)^{2}+i^{2}=25

This is the equation of circle with center (5,0)

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