Since ,it is a purely rectitude,that means in the current in the circuit and in voltage are in phase to each other so;the power factor becomes 1 you can also think of power factor as being the ratio of purely restitive circuit and the given circuit with same current flowing now the given circuit is a purely restitive one so the ratio is 1

The power factor of a pure resistor circuit is 1.

Explanation:

A pure resistor circuit consists of only resistive elements and does not include any capacitors or inductors. In such a circuit, the current is in phase with the voltage. This means that the voltage and current waveforms reach their maximum and minimum values at the same time.

- Definition of power factor: The power factor of an AC circuit is the ratio of the real power (in watts) to the apparent power (in volt-amperes). It is a measure of how effectively the circuit converts the electrical energy into useful work.
- Real power (P): It is the power that is actually consumed or dissipated in the circuit. It is given by the product of voltage, current, and the cosine of the phase angle between them.
- Apparent power (S): It is the product of voltage and current and represents the total power delivered to the circuit.
- Power factor (PF): It is the ratio of real power to apparent power, given by PF = P/S.

In a pure resistor circuit, the phase angle between the voltage and current is zero. This means that the cosine of the phase angle is equal to 1. As a result, the power factor is equal to 1.

- In a pure resistor circuit, the current and voltage waveforms are in phase with each other.
- The power factor in such a circuit is 1, indicating that the circuit is highly efficient in converting electrical energy into useful work.
- A power factor of 1 means that there is no reactive power in the circuit, and all the power is used to perform useful work.
- In practical applications, a power factor of 1 is desirable as it minimizes energy losses and ensures efficient operation of the circuit.

Therefore, the correct answer is option 'A' - One.