The power factor of an AC circuit has the value:

Explanation

The power factor (PF) of an AC circuit is the cosine of the angle between the voltage and current waveforms. It is given by the formula:[ {Power Factor (PF)} = cos(phi) ]where ( phi ) is the phase angle between voltage and current.In an ideal resistor, the voltage and current are in phase, and the power factor is 1 (unity). So, the correct answer is (b) Unity when the circuit contains only a resistance.Let's briefly discuss the other options:- (a) Unity when the circuit contains only an inductance: This is not correct. In an inductive circuit, the current lags behind the voltage, leading to a power factor less than 1.- (c) Unity when the circuit contains resistance and capacitor: This is not correct. The presence of both resistance and capacitance can result in a power factor less than 1, depending on the relative magnitudes and phase angles of the components.- (d) Unity when the circuit contains only a capacitance: This is not correct. In a capacitive circuit, the current leads the voltage, resulting in a power factor less than 1.So, the correct answer is (b) Unity when the circuit contains only a resistance.