Question

QUESTION 1 Consider the crout diagram n Figure 1, R=10?·Le 100 mH and the thynstor s trggered after a delay of radans. V,-220 v 50 Hz. 1.1 Determine how many radians the current will flow in each cycle of the supply Hint ?"," sin(ax + ?-9)-(1-sin(a-?),T 12 Sketch labelled waveforms of Ve. i, and V. 13 Calculate the average load voltage 14 Calculate the average load current [18] V. V. Figure 1

Answer 1

When diode is ON di/dt + R/L io = vm/L sin wt dy/dx py = Q integrating factor = e^integral p dx solution y(I. F) = integral Q(I. F) dx + k I. F = e^integral R/L dt = e^R/L t solution to the differential equation is e^R/L t = integral v_m/L sin cet e^R/L t dt + k integral e6ax sinbx dx e6ax/a^2 + b^2 [a sinbx - b cosbx] = e^ax/squareroot a^2 + b^2[a/squareroot a^2 + b^2 sinbx - b/squareroot a^2 + b^2 cos bx] = e^ax/squareroot a^2 + b^2 cos bx sin(bx - theta) theta = tan^-1 b/a a = R/L: b = w i_0 e^+ R/L t = v_m/L e^R/L t/squareroot (R/L) ^2 + w^2 sin (wt - theta) + k i_0 = v_m/L k/ squareroot r^2 + (wL) ^2 sin(wt - theta) + ke^-R/L t using intial condition i_0 = 0 at wt = alpha 0 = v_m/squareroot R^2 + (wL) ^2 sin (d - theta) + ke^-R/L d/w