In the measurement of three phase power by two wattmeter method, if the two wattmeter readings are equal then power factor of the circuit is 

Explanation:

Measurement of Three-Phase Power using the Two Wattmeter Method

Introduction: The two wattmeter method is a widely used technique for measuring the total power in a three-phase system. It is particularly suitable for balanced and unbalanced loads. The method involves the use of two wattmeters connected to the system, and the readings of these wattmeters help determine the total power and the power factor of the system.

Condition: When the two wattmeter readings are equal, the power factor of the circuit is unity (1). This occurs because the phase angle between the line voltage and current in the system is zero, indicating a purely resistive load. Let us delve deeper into the working principle and analysis to understand why this happens.

Working Principle:

In the two wattmeter method:

• Wattmeter 1 measures the power in one phase (P1).
• Wattmeter 2 measures the power in another phase (P2).
• The total power in the system is given by the sum of the readings of the two wattmeters: P = P1 + P2.

For a three-phase system with a balanced load, the power factor can be determined using the formula:

Power Factor (cos φ) = (P1 - P2) / (P1 + P2)

Analysis for Unity Power Factor:

When the power factor is unity (1), it implies that the load is purely resistive. In this case, the current and voltage are in phase, and the phase angle φ is zero. Substituting this condition into the formula:

• P1 = P2 (since both wattmeter readings are equal for a purely resistive load).
• cos φ = (P1 - P2) / (P1 + P2).
• cos φ = (P1 - P1) / (P1 + P1) = 0 / 2P1 = 0.

Thus, the power factor of the circuit is unity (cos φ = 1) when the two wattmeter readings are equal. This is a unique condition that arises due to the absence of any phase difference between the voltage and current.

Advantages of Two Wattmeter Method:

• Applicable for both balanced and unbalanced loads.
• Simple and effective for three-phase power measurement.
• Provides a direct way to measure power factor.

Correct Option Analysis:

The correct option is:

Option 2: Unity

This option is correct because the power factor of the circuit is unity when the two wattmeter readings are equal. The condition of equal readings arises when the load is purely resistive, and the current and voltage are in phase.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 0.8 lag

This option is incorrect. When the power factor is 0.8 lag, the phase angle is not zero, and the wattmeter readings will not be equal. Instead, one wattmeter will record a higher value than the other, depending on the phase angle of the load.

Option 3: 0.8 lead

Similar to option 1, this option is also incorrect. A power factor of 0.8 lead indicates a capacitive load, where the current leads the voltage. In this case, the wattmeter readings will again be unequal, and the condition of equal readings will not be satisfied.

Option 4: Zero

This option is incorrect because a power factor of zero implies a completely reactive load (either inductive or capacitive). In such a scenario, the current and voltage are 90° out of phase, and the two wattmeter readings will not be equal. Instead, one wattmeter may show a negative reading depending on the connection.

Conclusion:

The two wattmeter method is a reliable technique for measuring three-phase power and determining the power factor of a circuit. When the two wattmeter readings are equal, it indicates that the power factor of the circuit is unity, corresponding to a purely resistive load. This condition is unique and helps distinguish purely resistive loads from other types of loads in three-phase systems.