Question

A 236-V (rms), 60-Hz source supplies a parallel combination of a 5-kW heater and a 30-kVA induction motor whose power factor is 0.82 . Determine the system apparent power. The system apparent power is ___ kVA.

Answer 1

The system apparent power is 29.600 kVA.

Step-by-step explanation:

To determine the system apparent power, we need to calculate the apparent power for each device separately and then add them together. The apparent power is calculated using the formula S = VI, where S is apparent power in VA (volt-amps), V is voltage in volts, and I is current in amps.

For the 5-kW heater, the apparent power is S1 = 5000 VA.

For the 30-kVA induction motor with a power factor of 0.82, the real power can be calculated as P = S * power factor. Therefore, the real power for the motor is P2 = 30 kVA * 0.82 = 24.6 kW = 24,600 VA.

Adding the apparent powers of both devices gives the system apparent power: Ssystem = S1 + S2 = 5000 VA + 24,600 VA = 29,600 VA.