A closed circuit consists of a source of constant `emf E` 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 `L=0` the choke coil inductance was decreased abruptly `4` times.The current in the circuit as a function of time `t` is `E/R[1-xc^(-4tR//L)]`.Find out value of `x`.

Answer

C

Explanation

We write the equation of the circuit as `Ri+L/eta(di)/(dt)=xi`
For `t le 0`.The current at `t=0` just after inductance is changed is `i=etaxi/R`, so that the flux through the inductance is unchanged We look for a solution of the above equation in the form `i=A+Be^(-t//C)`
substituting `C=L/(etaR),B=eta-1,A=xi/R`.
Thus,`i=xi/R(1+(eta-1)e^(-eta Rt//L))`.
Put values `x=3`