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Question

A closed circuit consists of a source of constant emf xi and a choke coil of inductance L connected in series. The active resistance of the whole circuit is equal to R. It is in steady state. At the moment t=0 the choke coil inductance was decreased abruptly 4 times its initial value. The current in the circuit as a function of time t is ξ/R[1+xe4tR/L]. Find out value of x_______

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Solution

Let us say, inductance reduces by η times the initial value and ξ be the emf applied

We write the equation of the circuit as, Ri+Lηdidt=ξ

for t0.

The current at t=0 just after inductance is changed, is i=ηξR, so that the flux through the inductance is unchanged.

We look for a solution of the above equation in the form
i=A+Bet/C

substituting C=LηR, B=η1, A=ξR gives,

i=ξR(1+(η1)eηRt/L).

By putting x=3, the above equation becomes equation given in the question.

Accepted answers : 3 , 3.0 , 3.00

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