All Problems

Electromagnetic Induction. Maxwells Equations

Problem 3.326

A closed circuit consists of a source of constant emt B\mathscr{B} and a choke coil of inductance LL connected in series. The active resistance of the whole circuit is equal to R.R . At the moment t=0t=0 the choke coil inductance was decreased abruptly \eta times. Find the current in the circuit as a function of time tt.

Instruction. During a stepwise change of industance the total magnetic flux (flux linkage) remains constant.

Reveal Answer
I=ER[1+(η1)etηR/L]I=\frac{\mathscr{E}}{R}\left[1+(\eta-1) \mathrm{e}^{-t \eta R / L}\right]