What are the signs of wattmeter W1 and W2 , respectively, if the power factor of the system is 0.5?

The correct answer is option 4):

Concept:

Two wattmeter method:

• The two-wattmeter method uses two voltage measurements referenced to the same phase (line) and the two currents flowing into that phase. The assumption is that the three-phase system is balanced, i.e., the summation of all voltages = 0 V and the summation of all currents = 0 A.
• This is true if there is no leakage current from neutral to ground.

Reading of both wattmeters are

W₁ = √3 V_pI_pcos (30 - ϕ )

W₂ = √3 V_pI_pcos (30 + ϕ)

where V_p → Voltage across pressure coil I

p → Current through coil ϕ → Phase angle

\(\mathrm{Power\, Factor} = \cos \phi = \cos\left [ \tan^{-1}\sqrt{3}\left ( \frac{w_{1}-w_{2}}{w_{1}+w_{2}} \right ) \right ]\)

• The result can be summarised as At zero power factor lagging, W1 reads the positive value and W2 reads the negative value.
• For power factors lying between 0 to 0.5 lagging, W1 reads the positive value and W2 reads the negative value.
• At 0.5 power factor lagging, W1 reads the positive value and W2 reads the zero value.Hence option 4 is correct
• For power factors lying between 0.5 to 1 lagging, W1 reads the positive value and W2 reads the positive value.
• At unity power factor lagging, W1 reads the positive value and W2 reads the positive value.