Question

A closed circuit consits of a source of constant and `E` and a choke coil of inductance `L` connected in series. The active resistance of the whole circuit is equal to `R`. At the moment `t = 0` the choke coil inductance was decreased abrupty `eta` times. FInd the current in the circuit as a function of time `t`.

Answer 1

We write the equaction of the circuit as,
`Ri + (L)/(eta) (di)/(dt) = xi`
for `t ge 0`. The current at `t = 0` just after inductance is changed, is
`i = eta (xi)/(R)`,so that the flux through the inducatance is uncharged.
We look for a solution of the above equaction in the form
`i = A + B e^(t//C)`
Substitutaing `C = (L)/(eta R) , B = eta - 1, A = (xi)/(R)`
Thus, `i = (xi)/(R) (1 + (eta - 1) e^(-eta R t//L))`