Question

For the network shown in Figure 1. a) Find the impedances Zi. and Zc. (2 points) b) Find the total admittance and impedance in polar form. (2 points) c) Find the voltage E. (1 point) d) Find the currents IR, IL and Ic in polar form. (3 points) e) Find the average power delivered to the network. (2 points) is = 20 × 10-3 A cos(377t + 60°) 0.47 uF 2.5 H gure 1

Answer 1

i_3 = 20 times 10^- 3 cos (377 t + 60 degree) # current source is = 20 times 10^- 3 cos (377 t + 60 degree) generalize of current i = I_max cos (wt + emptyset) compare above two expression implies I_max = 20 times 10^- 3 Amp implies w = 377 rad/sec (a) Impedance Z_L = jwL Z_L = j377 times 2.5 = j942.5 Z_L = j942.5 ohm Z_L = 942.5 angle 90 degree ohm \r\n impedance Z_c = -j 1/wc Z_c = -j/377 times 0.47 times 10^- 6 Z_c = -j 5643.65935 ohm Z_c = 5643.6535 angle - 90 degree ohm (b) R, L and C in parallel then implies Total impedance Z = R parallel Z_c parallel Z_L implies Z = R parallel (Z_c times Z_L/Z_c + Z_L) implies Z = R parallel ((1131.45472 j)) implies z = 2000 times 1181.45472 j/2000 + 1131.45472j implies Z = 484.9029 + 857.13185j ohm