LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
509 views
in Electronics by (110k points)
closed by

 In 3-phase power measurement by two-wattmeter method, the two wattmeters read as W1 = 300 W and W2 = 300 W. Then the load is said to be operating at _________.


1. Unity power factor
2. Lagging power factor
3. Zero power factor
4. Leading power factor

1 Answer

0 votes
by (59.9k points)
selected by
 
Best answer
Correct Answer - Option 1 : Unity power factor

Concept:

In two wattmeter method, the power factor is given by

\(cosϕ = \cos \left[ {{{\tan }^{ - 1}}\left( {\frac{{\sqrt 3 \left( {{W_1} - {W_2}} \right)}}{{{W_1} + {W_2}}}} \right)} \right]\)

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

W1 = reading of 1st wattmeter

W2 = reading of 2nd wattmeter

When both the wattmeter’s show the same positive reading, ϕ becomes zero and hence power factor is unity.

Calculation:

Given that

W1 = 300 Watt and W2 = 300 Watt

Now power factor

\(\cosϕ = \cos \left[ {{{\tan }^{ - 1}}\left( {\frac{{\sqrt 3 \left( {{W_1} - {W_2}} \right)}}{{{W_1} + {W_2}}}} \right)} \right]\)

cos ϕ = 1 (Unity power factor)

 

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

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

W= 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

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...