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Two coils, 1 & 2, have a mutual inductan...

Two coils, 1 & 2, have a mutual inductance = M and resistances R each. A current flows in coil 1, which varies with time as: `I_(1)=kt^(2)`, where K is a constant and 't' is time. Find the totalcharge that has flown through coil 2, between t=0 and t=T.

Text Solution

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The correct Answer is:
`kMT^(2)//(R )`
`phi_(2)=MI_(1)=Mkt^(2)` and `e_(2)=(dphi_(2))/(dt)=d/(dt)Mkt^(2)`
`e_(2)=mk(dt^(2))/(dt)=Mk2t` and `I_(2)=e_(2)/R=(2Mkt)/R`
`Deltaq_(2)=int_(0)^(T)I_(2)dt=(2Mk)/R int_(0)^(T)tdt=(2Mk)/R[t^(2)/2]_(0)^(T)`
`=(MkT^(2))/R`
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