UPSC Exam > UPSC Questions > 37. In a series LCR circuit, the inductive re...
Start Learning for Free
37. In a series LCR circuit, the inductive reactance
(XL) is 10 2 and the capacitive reactance (Xc)
is 4 9. The resistance (R) in the circuit is 6 S2.
The power factor of the circuit is:
JEE (Main)-2021]?
(XL) is 10 2 and the capacitive reactance (Xc)
is 4 9. The resistance (R) in the circuit is 6 S2.
The power factor of the circuit is:
JEE (Main)-2021]?
Most Upvoted Answer
37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and t...
Given Data
- Inductive Reactance (XL) = 10 Ω
- Capacitive Reactance (XC) = 4 Ω
- Resistance (R) = 6 Ω
Power Factor Calculation
To find the power factor (PF) of a series LCR circuit, we first need to determine the total impedance (Z) and the phase angle (φ).
1. Calculate Net Reactance (X)
The net reactance (X) is given by:
\[
X = XL - XC
\]
Substituting the values:
\[
X = 10 - 4 = 6 Ω
\]
2. Calculate Total Impedance (Z)
The total impedance (Z) of the circuit can be calculated using the formula:
\[
Z = \sqrt{R^2 + X^2}
\]
Substituting the values:
\[
Z = \sqrt{6^2 + 6^2} = \sqrt{36 + 36} = \sqrt{72} = 6\sqrt{2} ≈ 8.49 Ω
\]
3. Calculate Power Factor (PF)
The power factor is defined as:
\[
PF = \cos(φ) = \frac{R}{Z}
\]
Substituting the values:
\[
PF = \frac{6}{8.49} ≈ 0.707
\]
Conclusion
Thus, the power factor of the circuit is approximately 0.707, indicating that the circuit has a balanced resistive and reactive component, common in LCR circuits.
- Inductive Reactance (XL) = 10 Ω
- Capacitive Reactance (XC) = 4 Ω
- Resistance (R) = 6 Ω
Power Factor Calculation
To find the power factor (PF) of a series LCR circuit, we first need to determine the total impedance (Z) and the phase angle (φ).
1. Calculate Net Reactance (X)
The net reactance (X) is given by:
\[
X = XL - XC
\]
Substituting the values:
\[
X = 10 - 4 = 6 Ω
\]
2. Calculate Total Impedance (Z)
The total impedance (Z) of the circuit can be calculated using the formula:
\[
Z = \sqrt{R^2 + X^2}
\]
Substituting the values:
\[
Z = \sqrt{6^2 + 6^2} = \sqrt{36 + 36} = \sqrt{72} = 6\sqrt{2} ≈ 8.49 Ω
\]
3. Calculate Power Factor (PF)
The power factor is defined as:
\[
PF = \cos(φ) = \frac{R}{Z}
\]
Substituting the values:
\[
PF = \frac{6}{8.49} ≈ 0.707
\]
Conclusion
Thus, the power factor of the circuit is approximately 0.707, indicating that the circuit has a balanced resistive and reactive component, common in LCR circuits.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]?
Question Description
37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]?.
37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]?.
Solutions for 37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of 37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]? defined & explained in the simplest way possible. Besides giving the explanation of
37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]?, a detailed solution for 37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]? has been provided alongside types of 37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]? theory, EduRev gives you an
ample number of questions to practice 37. In a series LCR circuit, the inductive reactance(XL) is 10 2 and the capacitive reactance (Xc)is 4 9. The resistance (R) in the circuit is 6 S2.The power factor of the circuit is:JEE (Main)-2021]? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup