Explanation:

Negative power indicates that the power is being returned to the source instead of being consumed by the load. This happens when the load is inductive, i.e., the current lags behind the voltage.

The power factor angle is the angle between the voltage and current phasors in an ac circuit. It is given by:

cos φ = P / (VI)

where φ is the power factor angle, P is the active power, V is the voltage, and I is the current.

Since the power is negative for 2 milliseconds in one cycle, the load is returning power to the source during that period. This means that the current is lagging behind the voltage, and the power factor angle is greater than 0°.

To find the power factor angle, we need to know the time delay between the voltage and current waveforms. This can be done by measuring the phase shift between the voltage and current using an oscilloscope or a power analyzer.

Assuming that the load is purely resistive for the rest of the cycle, the average power over one cycle should be zero. Therefore, the negative power during the 2 milliseconds should be compensated by positive power during the remaining time.

Let us assume that the load has an impedance Z = R + jX, where R is the resistance and X is the reactance. The power factor angle can be calculated as follows:

cos φ = (P1 - P2) / (Veff Ieff)

where P1 is the active power during the positive phase, P2 is the active power during the negative phase, Veff is the effective voltage, and Ieff is the effective current.

Since the load is purely resistive during the positive phase, P1 = VI cos φ1, where φ1 is the power factor angle during the positive phase. Therefore, cos φ1 = P1 / (VI).

During the negative phase, the power is negative, and the load is returning power to the source. Therefore, P2 = -VI cos φ2, where φ2 is the power factor angle during the negative phase. Therefore, cos φ2 = -P2 / (VI).

Since the average power over one cycle is zero, we have:

(P1 - P2) / 2 = 0

Therefore, P1 = P2 = P/2, where P is the active power over one cycle.

Substituting the values of P1 and P2, we get:

cos φ = P / (2Veff Ieff)

= -P / (2Veff Ieff) (since P2 is negative)

= -cos φ2 / 2

Therefore, cos φ2 = -2 cos φ

Since the power factor angle is greater than 0°, cos φ2 is negative. Therefore, cos φ must be positive, and the power factor angle must be between 0° and 90°.

The options given are:

a)9°

b)18°

c)36°

d)45°

The correct answer is option 'C', 36°, since it lies in the range of 0° to 90°.