Two wattmeters are connected to measure power in a three-phase system. Reading of one of the wattmeter is zero. Then power factor of the three-phase load is:

Explanation:

In a three-phase system, power measurement using two wattmeters is a common method known as the two-wattmeter method. This method is widely used for measuring power in both balanced and unbalanced three-phase systems. To understand the situation where one of the wattmeters reads zero, we need to delve into the principles of this method and the relationship between the readings and the power factor of the load.

Two-Wattmeter Method:

The two-wattmeter method involves connecting two wattmeters to a three-phase system to measure power. The readings of the two wattmeters (W1 and W2) can be used to determine the total power (P) and the power factor (pf) of the system. The total power is given by the sum of the readings:

P = W1 + W2

The power factor can be determined using the difference between the readings:

pf = cos(Φ) = (W1 - W2) / (W1 + W2)

Where Φ is the phase angle between the line voltage and the line current.

Scenario Analysis:

In the scenario where one of the wattmeters reads zero, let's assume that W1 = 0. This means that the entire power is being measured by the second wattmeter (W2). Therefore, the total power (P) is:

P = W1 + W2 = 0 + W2 = W2

Now, using the formula for power factor:

pf = cos(Φ) = (W1 - W2) / (W1 + W2) = (0 - W2) / (0 + W2) = -W2 / W2 = -1

However, the power factor cannot be -1 because it represents a purely inductive load, which is not possible in this context. Therefore, we need to consider the magnitude of the power factor:

|pf| = |cos(Φ)| = |-1| = 1

This represents a power factor of unity, which means the load is purely resistive. However, this is a theoretical consideration. Practically, the power factor can be determined by the specific configuration of the load and the readings of the wattmeters.

In a balanced three-phase system, if one of the wattmeters reads zero, it indicates that the load has a power factor of 0.5. This situation arises because the angle between the voltage and the current is 60 degrees (cos(60) = 0.5). Therefore, the correct power factor in this scenario is:

Correct Option: 0.5

The correct answer is option 3, which indicates that the power factor of the three-phase load is 0.5.

Additional Information

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

Option 1: Zero

If the power factor were zero, it would imply that the load is purely reactive (either inductive or capacitive), and no real power is being consumed. This would mean that both wattmeters should read zero, which is not the case here.

Option 2: Unity

A unity power factor (pf = 1) indicates a purely resistive load where the voltage and current are in phase. In such a case, both wattmeters would have equal readings, and neither would read zero. Therefore, this option is incorrect.

Option 4: 0.707

This value corresponds to a power factor angle of 45 degrees (cos(45) = 0.707). For this power factor, the readings of the two wattmeters would be different but not zero. Therefore, this option is incorrect.

Conclusion:

Understanding the two-wattmeter method and the relationship between the wattmeter readings and the power factor is crucial for accurately determining the power factor of a three-phase load. In this case, when one of the wattmeters reads zero, the power factor of the load is 0.5, which corresponds to an angle of 60 degrees between the voltage and the current. This analysis helps in correctly identifying the operating conditions of the three-phase system.