Question

4. Assuming that the switch has been open for a long time, find i) for >0. 800 0 30 v ve325 H a) Find the roots of the characteristic equation: b) Write the general form of the solution (with unknown constants) o(t) What is the value at time infnity? c) d) What is the value at time zero? e) What is the value of the derivative at time zero? What is the final solution? f)
please show your work and label your answers, thanks in advance!

Answer 1

If you like my work please upvote ?

Given circuit equation of force R +(Y_sc + SL/SL + 1/sc R + SL/S^2LC + 1 S^2LCR + R + SL = 0 Characteristic equation is S^2 + 1/RC S + 1/LC = 0 { R = 800 ohm L = 25 H C = 6.25 times 10^- 6 F S^2 + 1/800 times 6.25 times 10^-6 times S + 1/25 times 6025 times 10^- 6 = 0 S^2 + 200S + 6400 = 0 It is of form S^2 + 2 epsilon w_n S + w^2_n = 0 epsilon w_n = 100 T = 10 m Sec T = 1/epsilon w_n = 0.01 t = 10 m sec (1) implies S_1, 2 = -b plusminus squareroot b62 - 4ac/2a a) general form of I_0(f) I_0(t) = I(infinity) + [I(0) - I(infinity)]e^-t/T (c) I(infinity) = ? At t = infinity: capacitor open circuits inductor short circuits I(infinity) = 300/800 = 37.5 mA