Question

Question # 3 R1 100? S1 L1 2) Key Space R3 10mH R2 V1 For the circuit shown in the above figure, R3 is unkown: With the switch "S1" closed to position (2) and no currents in the circuit. The switch's position is changed from position (2) to position (1) at t-0. After a long time the circuit reaches a steady state condition. Calculate the steady state current in the inductance. 2) With the switch "S" closed to position (1) and the circuit is at steady stae. The switch's position is changed from position (1) to position (2). Calculate the energy dissipated in R3 from the time of closing the switch to position (2) to the zero current in the circuit.

Answer 1

"Given data t < 0: - switch at position 2: - rightarrow i_L(0) = 0 Amps t = alpha: - switch at position 1: - rightarrow system in steady state rightarrow Inductor rightarrow short I_L(alpha) = 100/(100)(100) = 100/50 rightarrow I_L(alpha) = 2 Amps t > 0: - Time Constant rightarrow switch at position 1 rightarrow voltage rightarrow short R = 50 omega L = 100 mit Time Constant N = 1/R rightarrow tau = 100 times 10^-5/50 rightarrow tau = 2 M sec \r\n current""- i_L(t) = i(alpha) + (i(0) - i(alpha))e^-t/tau = 2 + (0 - 2)e^-t/2 M rightarrow i_L(t) = 2(1 - e^-(500)t, Amps Energy dissipation rightarrow P = I^2 times R There is No-current rightarrow P = (Q)^2 times R_3 flow in 'R_3' Resistor rightarrow P = 0 W so No-power dissipation \r\n Note: - If anything wrong in Answer. Please leave a connect. I will do it again Thank you "