Step 1: Calculate the current IaA
The current IaA flows through the 5-ohm resistor and the impedance between nodes a and A. The impedance
between a and A is 5 - j6 + 5 = 10 - j6 ohms. The voltage across this impedance is 100/0° V.
IaA = (100∠0°) / (10 - j6) = 100 / √(10² + 6²) ∠arctan(6/10) = 100 / √(136) ∠30.964° = 8.575∠30.964° A
Step 2: Calculate the power absorbed by the X-Ω resistor (5-Ω resistor)
The current through the 5-Ω resistor is the magnitude of IaA, which is 8.575 A.
Power = I²R = (8.575)² * 5 = 73.53 W * 5 = 367.65 W
Step 3: Calculate the current IbB
The current IbB flows through the 5-ohm resistor and the impedance between nodes b and B. The impedance
between b and B is 5 + 8 = 13 ohms. The voltage across this impedance is 100/-120° V.
IbB = (100∠-120°) / 13 = 7.692∠-120° A
Step 4: Calculate the power absorbed by the Y-Ω resistor (8-Ω resistor)
The current through the 8-Ω resistor is the magnitude of IbB, which is 7.692 A.
Power = I²R = (7.692)² * 8 = 59.17 * 8 = 473.36 W
Step 5: Calculate the current Icc
The current Icc flows through the 5-ohm resistor and the impedance between nodes c and C. The impedance
between c and C is 5 + j3 + 10 = 15 + j3 ohms. The voltage across this impedance is 100/120° V.
Icc = (100∠120°) / (15 + j3) = 100 / √(15² + 3²) ∠(120° - arctan(3/15)) = 100 / √(234) ∠(120° - 11.31°) =
6.532∠108.69° A