When two-wattmeter method of measurement of power is used to measure power in a balanced three-phase circuit, if the wattmeter readings are zero and positive maximum respectively, then

Concept:

In a two-wattmeter method,

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

The reading of the 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

\(\phi = {\rm{ta}}{{\rm{n}}^{ - 1}}\left( {\frac{{\sqrt 3 \left( {{W_1} - {W_2}} \right)}}{{{W_1} + {W_2}}}} \right)\)

Calculation:

Given that, W1 = 0 kW

W2 = W kW

⇒ W1 + W2 = 0 + W = W kW

⇒ W1 - W2 = 0 - W = - W kW

\(\phi = {\rm{ta}}{{\rm{n}}^{ - 1}}\left( {\frac{{\sqrt 3 \left( {{W_1} - {W_2}} \right)}}{{{W_1} + {W_2}}}} \right)={\rm{ta}}{{\rm{n}}^{ - 1}}\left( {\frac{{\sqrt 3 \left( {-W} \right)}}{{W}}} \right)={\rm{ta}}{{\rm{n}}^{ - 1}}(-\sqrt 3)= - 60 ^\circ\)

Power factor = cos ϕ = cos (- 60°) = 0.5 (lag)

∴ The power factor is 0.5 lagging.

Important Points