UPSC Exam > UPSC Questions > 37. In a series LCR circuit, the inductive re...
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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.
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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.
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