Which condition is created by two wattmeters W1 and W2 for power factor is zero? 

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  1. W1 = W2 
  2. 2W1 = W2 
  3. W1 = 0
  4. W1 = -Ve W2  = +Ve 

Answer (Detailed Solution Below)

Option 4 : W1 = -Ve W2  = +Ve 
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Detailed Solution

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Measurement of power

According to Blondel's Theorem, for the measurement of power in n-phase, n-wire without neutral, (n - 1) wattmeters are required.

For measurement of power in 3-phase, (3 - 1 = 2) wattmeters are required.

The readings of both the wattmeters are given by:

\(W_1=V_LI_Lcos(30+ϕ)\)

\(W_2=V_LI_Lcos(30-ϕ)\)

The power factor is given by:

Power factor = cosϕ 

At zero power, cosϕ = 0

At, ϕ = 90°, the readings of both the wattmeters are:

\(W_1=V_LI_Lcos(30+90)={-0.5V_LI_L}\)

\(W_2=V_LI_Lcos(30-90)={+0.5V_LI_L}\)

Thus, W1 = -ve, W2  = +Ve 

Thus at zero power factor, the reading of both wattmeters are equal and opposite.

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