Question

Two wattmeters connected to measure the input to a balanced three-phase circuit indicate 2500 W and 500 W respectively.

Find the power factor of the circuit
(a) when both readings are positive
(b) when the latter reading is obtained after reversing the connections to the current coil of one instrument.

Answer 1

The power factor of the circuit when both readings are positive is approximately 0.894. When the latter reading is obtained after reversing the connections to the current coil of one instrument, the power factor is approximately 0.707.

Step-by-step explanation:

(a) To find the power factor of the circuit when both readings are positive, we can use the formula:

Power Factor = (P1 - P2) / √(P1^2 + P2^2)

Where P1 is the reading of the first wattmeter (2500 W) and P2 is the reading of the second wattmeter (500 W).

Substituting the values, we get:

Power Factor = (2500 - 500) / √(2500^2 + 500^2)

Calculating this, the power factor is approximately 0.894.

(b) When the latter reading is obtained after reversing the connections to the current coil of one instrument, the power factor can be found using the formula:

Power Factor = (P1 + P2) / √(P1^2 + P2^2)

Where P1 is the reading of the first wattmeter (2500 W) and P2 is the reading of the second wattmeter (-500 W).

Substituting the values, we get:

Power Factor = (2500 + (-500)) / √(2500^2 + (-500)^2)

Calculating this, the power factor is approximately 0.707.