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Question

The current in a coil of self inductance 5 H is increasing according to i=2sint2 . The amount of energy spent during the period when current changes from 0 to 2 ampere is

A
10 joule
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B
5 joule
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C
100 joule
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D
2 joule
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Solution

The correct option is B 10 joule
i=2sin(t2)
e=Ldidt=4Ltcos(t2)

Amount of energy spent during the period when current changes from 0 to 2 ampere,

=t=π/2t=0ei dt=t=π/2t=08Ltcos(t2)sin(t2) dt =t=π/2t=04Ltsin(2t2) dt
Let u=2t2 du=4tdt
t=π/2t=04Ltsin(2t2) dt=t=π/2t=0Lsin(u) du=2L= 10 joules

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