(a) contains a freewheeling diode Dm, commonly connected across an inductive load to provide a path for the current in the inductive load when the switch S is opened after time t (during which the switch was closed). Consider the circuit operation in two modes, with mode 1 beginning when the switch is closed at t = 0, and mode 2 starting when the switch is opened after the current i has reached its steady state in mode 1. Obtain the waveforms of the currents i(t) and if(t).

(b) Consider the energy-recovery diode circuit shown in Figure , alongwith a feed- backwinding.Assume the transformer to have a magnetizing inductance of Lm and an ideal turns ratio of a = N2/N1. Let mode 1 begin when the switch S is closed at t = 0, andmode 2 start at t = t1, when the switch is opened.

Let t₁ and t₂ be the durations ofmodes 1 and 2, respectively. Develop the equivalent circuits for the two modes of operation, and obtain the various waveforms for the currents and voltages.