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BSNL JE (TTA) 25 September 2016 Shift 1 Paper

Option 2 : 0

CT 1: Basic Concepts

18461

10 Questions
10 Marks
6 Mins

In two wattmeter method, the wattmeter readings are given by

W1 = VLIL cos (30 – ϕ)

W2 = VLIL cos (30 + ϕ)

Total power = W1 + W2

Reactive power = √3 (W1 – W2)

Power factor = cos ϕ

Where \(\phi = {\tan ^{ - 1}}\left( {\frac{{\sqrt 3 \left( {{W_1} - {W_2}} \right)}}{{\left( {{W_1} + {W_2}} \right)}}} \right)\)

Important Point:

p.f. angle (ϕ) |
p.f.(cos ϕ) |
W1 [VLIL cos (30 + ϕ)] |
W2 [VLIL cos (30 - ϕ)] |
W = W1 + W2 [W = √3VLIL cos ϕ] |
Observations |

0° |
1 |
\(\frac{{\sqrt 3 }}{2}{V_L}{I_L}\) |
\(\frac{{\sqrt 3 }}{2}{V_L}{I_L}\) |
√3 VLIL |
W1 = W2 |

30° |
0.866 |
\(\frac{{{V_L}I}}{2}\) |
VLIL |
1.5 VL IL |
W2 = 2W1 |

60° |
0.5 |
0 |
\(\frac{{\sqrt 3 }}{2}{V_L}{I_L}\) |
\(\frac{{\sqrt 3 }}{2}{V_L}{I_L}\) |
W1 = 0 |

90° |
0 |
\(\frac{{ - {V_L}{I_L}}}{2}\) |
\(\frac{{{V_L}{I_L}}}{2}\) |
0 |
W1 = -ve W2 = +ve |