A 3-phase, 500-V motor load has a power factor of 0.4 Two watt meters

1.	A 3-phase, 500-V motor load has a power factor of 0.4 Two watt meters connected to measure the power show the input to be 30 kW. Find the reading on each instrument.
Answer» tanφ = (√3(W₁ - W₂))/(W₁ + W₂) ....(i) Now, cosφ = 0.4; φ cos^-1(0.4) = 66.6°; tan 66.6° = 2.311 W₁ + W₂ = 30 ....(ii) Substituting these values in equation (i) above, we get 2.311 = (√3(W₁ - W₂))/30 ∴ W₁ - W₂ = 40 .... (iii) From Eq. (ii) and (iii), we have W₁ = 45 kW and W₂ = – 5 kW Since W₂ comes out to be negative, second watt meter reads ‘down scale’. Even otherwise it is obvious that p.f. being less than 0.5, W₂ must be negative.

A 3-phase, 500-V motor load has a power factor of 0.4 Two watt meters connected to measure the power show the input to be 30 kW. Find the reading on each instrument.

Answer»

tanφ = (√3(W₁ - W₂))/(W₁ + W₂) ....(i)

Now, cosφ = 0.4; φ cos^-1(0.4) = 66.6°; tan 66.6° = 2.311

W₁ + W₂ = 30 ....(ii)

Substituting these values in equation (i) above, we get

2.311 = (√3(W₁ - W₂))/30

∴ W₁ - W₂ = 40 .... (iii)

From Eq. (ii) and (iii), we have W₁ = 45 kW and W₂ = – 5 kW

Since W₂ comes out to be negative, second watt meter reads ‘down scale’. Even otherwise it is obvious that p.f. being less than 0.5, W₂ must be negative.

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A 3-phase, 500-V motor load has a power factor of 0.4 Two watt meters connected to measure the power show the input to be 30 kW. Find the reading on each instrument.

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