Question

Problem 11 () 2cos(5000t + 45) mA L 0.1H C 200nF R 7500 GV(t) G 0.5 V()L Is0)(T Consider the above circuit to be in steady state and determine the following: a) The average power received by each element? b) The reactive power received by each element? c) What do you notice about the kind of power that each element receives?? (Did a component receive only average/complex power or both? What kind of component it?) was

Answer 1

Given I_S (t) = 2 cos (5000 t + 45 degree) mA = 2 angle 45 mA W = 5000 rad/sec, L = 0.1 H, C = 200 n F, R = 750 ohm X_L = j WL = j times 5000 times 0.1 = j 500 ohm X_C = -j/W C = -j/5000 times 2005 = -j 1000 ohm Nodal analyst At node (1) v_1/j 500 + v_1 - v_2/- j100 - 2 angle 45 m - G v_x = 0 implies - j 2 m v_1 + j 10 m (v_1 - v_2) - 2 angle 45 m - 0.5 v_1 = 0 [because v_x = v] - j 2 v_1 + j 10 (v_1 - v_2) - 2 angle 45 - 500 v_1 = 0 (- 500 + j 8) v_1 - 510 v_2 = 2 angle - (1) At node (2) lambda v_x + v_2 - v_1/- j 100 + v_2/750 = 0 0.5 v_1 + j 10 m(v_2 - v_1) + 1.333 m v_2 = 0