Consider the half-wave, phase-controlled rectifier system of Figure. This is essentially the same circuit as that of Problem 10.8 with the exception that diode D1 of Figure has been replaced by an SCR, which you can consider to be ideal. Let R = 5? and V_s (t) = V₀ sin wt, where V₀ = 45 V and w = 100? rad/sec. Assume that the inductor L is sufficiently large such that w (L/R) >> 1 and that the SCR is triggered ON at time t_d (0 t_d ?/w).

a. Find an expression for the average (dc) value V_dc of the voltage v`_s (t) across the series resistor/inductor combination as a function of the delay time t_d.

b. Using the fact that, in the steady state, there will be zero average voltage across the inductor, find an expression for the dc inductor current I_dc, again as a function of the delay time t_d.

c. Plot Idc as a function of td for (0 t_d ?/w).

Transcribed Image Text:

i,() DI D2 Av) v,(t) v(1) TI v,(1) D2 A )