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Question

The potential difference across a 2H inductor as a function of time is shown in the figure. At t=0, current is zero. Choose the correct statement(s).


A
Current at t=2s is 5A
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B
Current at t=2s is 10A
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C
Current versus time graph across the inductor will be
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D
Current versus time graph across the inductor will be
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Solution

The correct options are
A Current at t=2s is 5A
C Current versus time graph across the inductor will be


We know that potential across inductor, V=LdIdt(1)
dI=20VdtL
Now 20Vdt= Area under the V-t graph for t=02 sec
Area, A=12×2×10=10
Therefore dI=I=AL=102=5 A
Hence option A is correct.
For current variation lets consider voltage variation in 2 cases i.e 0-2 sec and 2-4 sec.
Case 1: For t=02 sec
Equation of straight line passing through origin,
V=mt+C, where m is slope and C is y-intercept
From graph, m=tanθ=102=5 and C=0
Therefore, V=5t
Substituting V in equation (1) and integrating,
dI=VdtL
I=1L5tdt=5t22L
Its evident that the variation is not linear and hence option D is incorrect. Also the curve should show increasing slope from 0-2 sec.
Case 2: For t=24 sec
Variation of V with t can be given using staright line equation as,
V=5t+20
dI=VdtL
I=1L(5t+20)dt=1L(5t22+20t)
The above equation shows decreasing slope and so does the graph in option C. Hence option C is correct.

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