Question

Please show all work and concepts

5.2 (15 pts) In the following circuit, voltage source V 10020° V, 60 Hz supplies power to three load circuits with impedances Z1, Z2, and Z3. The following information was deduced from measurements performed on the three load circuits Load Z1: 45 W at pf 0.95 lagging Load Z2: 70 VA at pf 0.75 leading Load Z3: 100 VA at pf = 0.6 lagging (a) Are Z1, Z2, and Z3 inductive or capacitive? (b) Determine the equivalent impedance of the parallel combination. Is it inductive or capacitive? (c) Determine the parallel element required to achieve a unity power factor (pf 1) for the entire load. Hint: The complex power of total load is the sum of the complex powers contributed by individual loads

Answer 1

V_s = 100 < 0 60 Hz load Z_1 = usm pf = 0.9 s lagging load Z_2 = 70 uA pf = 0.75 leading load Z_3 = 100 uA pf = 0.6 lagging in lagging type load, inductance is dominat while in leading type load, capacitance is dominant. Z_1 = lagging rightarrow inductive Z_2 = leading rightarrow capacitive Z_3 = lagging rightarrow inductive equivalent impedance we have to calculate individual impedance power = V_cos phi us = 100 times I times 0.9s I = 0.4736 < - cos^-1 0.95 [I_1 = 0.4736 < -18.19 degree] Z_1 = v/I_1 = 100 < 0/0.4736 < -18.19 = 200.6 [Z_1 = 211.15 < 18.19] Z_2 p = 70 times 0.75 = 52.5 watt 52.s = 100 times I times 0.75 I_2 = 0.7 < cos^-1 0.75 [I_2 = 0.7 < 41.41 degree] Z_z = v/I_2 = 100/0.7 = 142.8s < - 41.41 degree