Final answer:
The capacitor required to correct the power factor to unity for an AC motor with given impedance can be calculated by finding a capacitive reactance equal to the motor's inductive reactance, and then solving for the capacitance.
Step-by-step explanation:
To determine the value of the capacitor required for power factor correction to unity in an AC motor, we must first understand that power factor correction involves the addition of a capacitor in parallel with a load to counteract the effect of the load's inductance. In an AC circuit, power factor (PF) is the ratio of the real power flowing to the load to the apparent power in the circuit. A PF of 1, or 'unity', means that all the power is being used effectively.
The motor's impedance is given as ZL = (5.6 + j2.20) Ω, where the reactive part (j2.20 Ω) is due to the inductance of the motor. The frequency of the source is 60 Hz, and the voltage is 220 V RMS. To correct the power factor to unity, we must add a capacitor with a reactance that is equal in magnitude but opposite in sign to the motor's inductive reactance.
The capacitive reactance (XC) can be calculated using the formula XC = 1 / (2πfC). To find C, we rearrange the formula to C = 1 / (2πfXC). Given that XC must equal 2.20 Ω at 60 Hz,
C = 1 / (2π(60 Hz)(2.20 Ω)).
Calculating this, we get the capacitance C in farads. To convert it to microfarads (μF), we multiply by 1,000,000.