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In LCR series a.c circuit, the phase difference between current and voltage is 300. The reactance of the circuit is 17.32 Ω The value of resistance is?
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In LCR series a.c circuit, the phase difference between current and vo...
Understanding the LCR Series Circuit
In an LCR (Inductor-Capacitor-Resistor) series circuit, the relationship between voltage and current is crucial in determining the overall behavior of the circuit. The phase difference between current and voltage indicates whether the circuit is inductive or capacitive.
Given Data
- Phase difference (φ) = 30 degrees
- Reactance (X) = 17.32 Ω
Calculating Resistance
To find the resistance (R) in the circuit, we can use the tangent of the phase angle:
- The formula relating phase angle to resistance and reactance is:
tan(φ) = X / R
- Rearranging gives us:
R = X / tan(φ)
Calculating tan(30 degrees)
- The value of tan(30 degrees) is √3/3, which is approximately 0.577.
Substituting Values
- Now, plug in the reactance value:
R = 17.32 / 0.577
- This gives R ≈ 30 Ω.
Conclusion
The resistance value in the LCR series circuit, with a phase difference of 30 degrees and a reactance of 17.32 Ω, is approximately:
- R ≈ 30 Ω
Understanding this relationship helps in analyzing the performance of the circuit under AC conditions and is essential for designing effective electrical systems.
In an LCR (Inductor-Capacitor-Resistor) series circuit, the relationship between voltage and current is crucial in determining the overall behavior of the circuit. The phase difference between current and voltage indicates whether the circuit is inductive or capacitive.
Given Data
- Phase difference (φ) = 30 degrees
- Reactance (X) = 17.32 Ω
Calculating Resistance
To find the resistance (R) in the circuit, we can use the tangent of the phase angle:
- The formula relating phase angle to resistance and reactance is:
tan(φ) = X / R
- Rearranging gives us:
R = X / tan(φ)
Calculating tan(30 degrees)
- The value of tan(30 degrees) is √3/3, which is approximately 0.577.
Substituting Values
- Now, plug in the reactance value:
R = 17.32 / 0.577
- This gives R ≈ 30 Ω.
Conclusion
The resistance value in the LCR series circuit, with a phase difference of 30 degrees and a reactance of 17.32 Ω, is approximately:
- R ≈ 30 Ω
Understanding this relationship helps in analyzing the performance of the circuit under AC conditions and is essential for designing effective electrical systems.
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In LCR series a.c circuit, the phase difference between current and voltage is 300. The reactance of the circuit is 17.32 Ω The value of resistance is?
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In LCR series a.c circuit, the phase difference between current and voltage is 300. The reactance of the circuit is 17.32 Ω The value of resistance is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In LCR series a.c circuit, the phase difference between current and voltage is 300. The reactance of the circuit is 17.32 Ω The value of resistance is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In LCR series a.c circuit, the phase difference between current and voltage is 300. The reactance of the circuit is 17.32 Ω The value of resistance is?.
In LCR series a.c circuit, the phase difference between current and voltage is 300. The reactance of the circuit is 17.32 Ω The value of resistance is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In LCR series a.c circuit, the phase difference between current and voltage is 300. The reactance of the circuit is 17.32 Ω The value of resistance is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In LCR series a.c circuit, the phase difference between current and voltage is 300. The reactance of the circuit is 17.32 Ω The value of resistance is?.
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