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The current in a coil of self inductance...

The current in a coil of self inductance 2.0 henry is increasing according to `i= 2 sin t^(2)` ampere. Find the amount of energy spent during the period when the current changes from 0 to 2 amp.

Text Solution

Verified by Experts

For `0=2sin t^(2)impliest=0`
and `2=2sin^(2)timpliest^(2)=(pi)/2`
`:.t=sqrt((pi)/2)` The energy spend `E=1/2 Li^(2)`
`=1/2L(2sin t^(2))^(2)`
`=2Lsin^(2)t`
`=2Lsin^(2)t`
`=2xx2sin^(2)pi//2=4J`
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