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The power of system, three-phase 10 kVA load with a power factor of 0.342, is measured by two-wattmeter method. The readings of two wattmeters are W1 and W2. What can be said about these readings?
1. When power factor is changed from lagging to leading, the reading of W1 and W2 increase.
2. When power factor is changed from lagging to leading, the reading of W1 and W2 get interchanged.
3. When power factor is changed from lagging to leading, the reading of W1 and W2 decrease.
4. When power factor is changed from lagging to leading, the reading of W1 and W2 attain negative sign, always.

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Correct Answer - Option 2 : When power factor is changed from lagging to leading, the reading of W1 and W2 get interchanged.

Concept:

Two-wattmeter method:

The reading of first wattmeter (W1) = VL IL cos (30 + ϕ)

The reading of second wattmeter (W2) = VL IL cos (30 - ϕ)

Total power in the circuit (P) = W1 + W2

Total reactive power in the circuit \(Q=\sqrt{3}\left( {{W}_{1}}-{{W}_{2}} \right)\)

Power factor = cos ϕ

\(ϕ =\text{ta}{{\text{n}}^{-1}}\left( \frac{\sqrt{3}\left( {{W}_{1}}-{{W}_{2}} \right)}{{{W}_{1}}+{{W}_{2}}} \right)\)

If,

W1 > W2: The power factor consider as lagging

W2 > W1: The power factor consider as leading

Hence, When the power factor is changed from lagging to leading, the reading of W1 and W2 get interchanged.

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