Question

Questions and answers are here, need solution process.
3. a) For the circuit shown in Figure Q3 (a): i) Find the mathematical expression for the transient behaviour of the voltage 6 vc across the capacitor and the current ic when the switch is moved into position 1 at t- 0 s ii) Find the mathematical expression for the response of vc and ic if the switch 4 is moved into position 2 at t charging phase) τ (where τ is the circuit time constant of the iii) Plot the waveforms obtained in parts i) and ii) on the same time axis for the 4 voltage vc and the current ic using the defined polarity and current direction as shown in Figure Q3 (a) 4 mA Figure Q3 (a) b) What causes transient in electrical circuits and networks? Why is it important to 3 study the transient behaviour? Give some relevant examples to support your answer. c) With the aid of detailed diagrams and equations, derive the transfer (T) 3 parameters. Use the transfer parameters to model a simple ideal transformer circuit.
​​​​​​​

Answer 1

By KVL in the circuit, 20 = 1(8k) + 1/c integral I dt differentiating w.r.t t 0 = 8k di/dt + i/c i(t) = V/R e^-t/RC (R = 8 k ohm c = 10 mu F) v_c = 1/c integral^t_0 id t V_c(t) = [V_c(o +) - V_c(infinity)] e^-t/RC + v_c (infinity) in the given circuit V_c(0^-) = V_c(0^+) = 0v V_c (infinity) = 20 v \r\n Fine constant z = RC = 8 times 10^3 times 10 times 10^-6 = 80 ms therefore from equation (1) v_c(t) = (0 - 20) e^-t/80 ms + 20 = 20 (1 - e^-t/80 ms) v from equation (ii) i_c (t) = 20/8 k e^-t/80 ms = (2.5 times 10^-3) r^-t/80 ms switch is moved to position (2) at f = z Equivalent circuit R_2 = 1 K ohm R_3 = 3 k ohm at t = z, V_c(t) = 20(1 - e^-z/z) = 20 (1 - e^-1) = 12.64 v time constant, z = 4 k ohm times