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Figure shows a circuit consisting of an ...

Figure shows a circuit consisting of an ideal cell, an inductor `L`, and a resistor `R`, connected in series. Let switch `S` be closed at `t = 0`. Suppose at `t = 0`, the current in the inductor is `i_(o)`, then find out the equation of current as a function of time.

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Let an instant t current in the circuit is `i` which is increasing at the rate di/dt.
Writing KCL along the circuit, we have `epsi-L(di)/(Dt)-iR=0`
`implies L(di)/(dt)=epsi-iRimplies int_(i_(0))^(i)(di)/(epsi-iR)=int_(0)^(t)(dt)/(L)`
`implies In ((epsi-iR)/(epsi-i_(0)R))=-(Rt)/(L) implies epsi-iR=(epsi-i_(0)R)e^(-Rt//L)implies i=(epsi-(epsi-i_(0)R)e^(-Rt//L))/( R)`
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