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A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,
respectively, the operating angular frequency (in rad/s) is ________.
respectively, the operating angular frequency (in rad/s) is ________.
Imp : you should answer only the numneric value
Correct answer is '0.45'. Can you explain this answer?
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Verified Answer
A series LCR circuit is operated at a frequency different from its res...
The operating frequency (wx), at which current leads the supply.
i.e., wx < wr
again magnitude of current is half the value at resonance
i.e., wx < wr
again magnitude of current is half the value at resonance
Most Upvoted Answer
A series LCR circuit is operated at a frequency different from its res...
Given:
L = 1 H
C = 1 F
R = 1 ??
Current at operating frequency = 1/2 * Current at resonance frequency
Approach:
To find the operating angular frequency, we need to know the relationship between the impedance and the phase angle in an LCR circuit. Since the current leads the supply voltage, the phase angle is negative.
Formula:
The impedance in an LCR circuit is given by:
Z = √(R^2 + (Xl - Xc)^2)
where Xl is the inductive reactance and Xc is the capacitive reactance.
The phase angle φ is given by:
tan φ = (Xl - Xc) / R
Calculations:
At resonance frequency:
Xl = ωL = 1ω
Xc = 1 / (ωC) = 1 / ω
Given that the current at operating frequency is half the value at resonance frequency, we can write:
I(operating) = 1/2 * I(resonance)
√(R^2 + (Xl(operating) - Xc(operating))^2) = 1/2 * √(R^2 + (Xl(resonance) - Xc(resonance))^2)
Since the value of R is not given, we need to find the relationship between Xl(operating) and Xc(operating).
From the formula for phase angle, we can write:
tan φ(operating) = (Xl(operating) - Xc(operating)) / R
Since the current leads the voltage, the phase angle φ(operating) is negative. So we have:
tan φ(operating) = -√(3) / 1 = -√(3)
Using the inverse tangent function, we can find the value of the phase angle φ(operating).
Now, we can substitute the values of Xl(operating), Xc(operating), and the phase angle φ(operating) into the impedance formula to solve for R.
Finally, we can substitute the obtained value of R into the formula for Xc(operating) and solve for ω(operating).
Answer:
The operating angular frequency (in rad/s) is approximately 0.45.
L = 1 H
C = 1 F
R = 1 ??
Current at operating frequency = 1/2 * Current at resonance frequency
Approach:
To find the operating angular frequency, we need to know the relationship between the impedance and the phase angle in an LCR circuit. Since the current leads the supply voltage, the phase angle is negative.
Formula:
The impedance in an LCR circuit is given by:
Z = √(R^2 + (Xl - Xc)^2)
where Xl is the inductive reactance and Xc is the capacitive reactance.
The phase angle φ is given by:
tan φ = (Xl - Xc) / R
Calculations:
At resonance frequency:
Xl = ωL = 1ω
Xc = 1 / (ωC) = 1 / ω
Given that the current at operating frequency is half the value at resonance frequency, we can write:
I(operating) = 1/2 * I(resonance)
√(R^2 + (Xl(operating) - Xc(operating))^2) = 1/2 * √(R^2 + (Xl(resonance) - Xc(resonance))^2)
Since the value of R is not given, we need to find the relationship between Xl(operating) and Xc(operating).
From the formula for phase angle, we can write:
tan φ(operating) = (Xl(operating) - Xc(operating)) / R
Since the current leads the voltage, the phase angle φ(operating) is negative. So we have:
tan φ(operating) = -√(3) / 1 = -√(3)
Using the inverse tangent function, we can find the value of the phase angle φ(operating).
Now, we can substitute the values of Xl(operating), Xc(operating), and the phase angle φ(operating) into the impedance formula to solve for R.
Finally, we can substitute the obtained value of R into the formula for Xc(operating) and solve for ω(operating).
Answer:
The operating angular frequency (in rad/s) is approximately 0.45.
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A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,respectively, the operating angular frequency (in rad/s) is ________.Imp : you should answer only the numneric valueCorrect answer is '0.45'. Can you explain this answer?
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A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,respectively, the operating angular frequency (in rad/s) is ________.Imp : you should answer only the numneric valueCorrect answer is '0.45'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,respectively, the operating angular frequency (in rad/s) is ________.Imp : you should answer only the numneric valueCorrect answer is '0.45'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,respectively, the operating angular frequency (in rad/s) is ________.Imp : you should answer only the numneric valueCorrect answer is '0.45'. Can you explain this answer?.
A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,respectively, the operating angular frequency (in rad/s) is ________.Imp : you should answer only the numneric valueCorrect answer is '0.45'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,respectively, the operating angular frequency (in rad/s) is ________.Imp : you should answer only the numneric valueCorrect answer is '0.45'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,respectively, the operating angular frequency (in rad/s) is ________.Imp : you should answer only the numneric valueCorrect answer is '0.45'. Can you explain this answer?.
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A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,respectively, the operating angular frequency (in rad/s) is ________.Imp : you should answer only the numneric valueCorrect answer is '0.45'. Can you explain this answer?, a detailed solution for A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,respectively, the operating angular frequency (in rad/s) is ________.Imp : you should answer only the numneric valueCorrect answer is '0.45'. Can you explain this answer? has been provided alongside types of A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,respectively, the operating angular frequency (in rad/s) is ________.Imp : you should answer only the numneric valueCorrect answer is '0.45'. Can you explain this answer? theory, EduRev gives you an
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