The current in a coil of self-inductance `2` H increases as `I=2sint^(2)`, where t stands for time. Find the amount of energy spent during a period when the current changes from zero to `2` A.

Explanation

Given current, `I=2sint^(2)`
`:.` Emf induced,
`epsilon=L(dI)/(dt)=Lxx(d)/(dt)(2sint^(2))`
`=Lxx2xx(2sint)xxcost=2Lsin2t`
`:.` Energy spent, dU=Vidt=epsilonIdt
implies dU=`2Lsin2txx2sint^(2)dt`
`:.` Total energy spent,
`U=int_(0)^(t)dU=4Lint_(0)^(t)sin2txxsint^(2)dt`