Physics Exam > Physics Questions > In an LCR circuit, the capacitance is made on...
Start Learning for Free
In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?
Correct answer is '4'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In an LCR circuit, the capacitance is made one - fourth when in resona...
At resonance ; XL = Xc
Now
Thus change in inductance should be 4 times.
Now
Thus change in inductance should be 4 times.
Most Upvoted Answer
In an LCR circuit, the capacitance is made one - fourth when in resona...
Resonance in an LCR circuit occurs when the inductive reactance (XL) and the capacitive reactance (XC) cancel each other out, resulting in a purely resistive impedance. This happens when the angular frequency of the circuit (ω) is equal to the resonant frequency (ω0), which can be calculated using the formula:
ω0 = 1/√(LC)
Where L is the inductance and C is the capacitance of the circuit.
In this question, we are given that the capacitance is decreased to one-fourth of its original value. Let's call the original capacitance C1 and the new capacitance C2 (C2 = C1/4). We need to find out how many times the inductance should be changed to keep the circuit in resonance.
Let's assume the original inductance is L1 and the new inductance is L2. We can write the resonant frequency for both cases as:
ω01 = 1/√(L1C1) (original resonant frequency)
ω02 = 1/√(L2C2) (new resonant frequency)
According to the given condition, the circuit remains in resonance even after changing the capacitance. This means that the resonant frequency remains the same. So we can write:
ω01 = ω02
Substituting the values of ω0 and the given expressions for C2:
1/√(L1C1) = 1/√(L2(C1/4))
Simplifying the equation by squaring both sides and cross-multiplying:
L1C1 = L2(C1/4)
4L1C1 = L2C1
Dividing both sides by C1:
4L1 = L2
So, we can see that the inductance needs to be changed to four times its original value (L2 = 4L1) in order to maintain resonance in the circuit when the capacitance is reduced to one-fourth. Therefore, the correct answer is 4.
ω0 = 1/√(LC)
Where L is the inductance and C is the capacitance of the circuit.
In this question, we are given that the capacitance is decreased to one-fourth of its original value. Let's call the original capacitance C1 and the new capacitance C2 (C2 = C1/4). We need to find out how many times the inductance should be changed to keep the circuit in resonance.
Let's assume the original inductance is L1 and the new inductance is L2. We can write the resonant frequency for both cases as:
ω01 = 1/√(L1C1) (original resonant frequency)
ω02 = 1/√(L2C2) (new resonant frequency)
According to the given condition, the circuit remains in resonance even after changing the capacitance. This means that the resonant frequency remains the same. So we can write:
ω01 = ω02
Substituting the values of ω0 and the given expressions for C2:
1/√(L1C1) = 1/√(L2(C1/4))
Simplifying the equation by squaring both sides and cross-multiplying:
L1C1 = L2(C1/4)
4L1C1 = L2C1
Dividing both sides by C1:
4L1 = L2
So, we can see that the inductance needs to be changed to four times its original value (L2 = 4L1) in order to maintain resonance in the circuit when the capacitance is reduced to one-fourth. Therefore, the correct answer is 4.
Free Test
FREE
| Start Free Test |
Community Answer
In an LCR circuit, the capacitance is made one - fourth when in resona...
At resonance ; XL = Xc
Now
Thus change in inductance should be 4 times.
Now
Thus change in inductance should be 4 times.
|
Explore Courses for Physics exam
|
|
Similar Physics Doubts
In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer?
Question Description
In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer?.
In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer?.
Solutions for In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
Here you can find the meaning of In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer?, a detailed solution for In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer? has been provided alongside types of In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In an LCR circuit, the capacitance is made one - fourth when in resonance, then how many times the inductance should be changed, so that the circuit remains in resonance?Correct answer is '4'. Can you explain this answer? tests, examples and also practice Physics tests.
|
|
Explore Courses for Physics 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup