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In LCR circuit, the capacitance is changed from C to 4 C. For the same resonant frequency, the F inductance should be changed from L to
- a)2 L
- b)L/2
- c)L/4
- d)4L
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In LCR circuit, the capacitance is changed from C to 4 C. For the same...
Explanation:
Resonant frequency (f) of a LCR circuit is given by:
f = 1/(2π√LC)
When capacitance is changed from C to 2C, the resonant frequency becomes:
f' = 1/(2π√L(2C))
To keep the resonant frequency unchanged, we need to have:
f = f'
Therefore,
1/(2π√LC) = 1/(2π√L(2C))
Simplifying the above equation, we get:
√2 = √(C/2C)
√2 = 1/√2
2 = C/2C
C = 4C/2
Therefore, capacitance is changed from C to 4C/2 = 2C.
Now, we need to find the new inductance (L') that will keep the resonant frequency unchanged.
f = f'
1/(2π√LC) = 1/(2π√L'C)
√(L'/L) = 2
L' = 4L
Therefore, the inductance should be changed from L to 4L/2 = L/2 to keep the resonant frequency unchanged when capacitance is changed from C to 2C.
Hence, option B is the correct answer.
Resonant frequency (f) of a LCR circuit is given by:
f = 1/(2π√LC)
When capacitance is changed from C to 2C, the resonant frequency becomes:
f' = 1/(2π√L(2C))
To keep the resonant frequency unchanged, we need to have:
f = f'
Therefore,
1/(2π√LC) = 1/(2π√L(2C))
Simplifying the above equation, we get:
√2 = √(C/2C)
√2 = 1/√2
2 = C/2C
C = 4C/2
Therefore, capacitance is changed from C to 4C/2 = 2C.
Now, we need to find the new inductance (L') that will keep the resonant frequency unchanged.
f = f'
1/(2π√LC) = 1/(2π√L'C)
√(L'/L) = 2
L' = 4L
Therefore, the inductance should be changed from L to 4L/2 = L/2 to keep the resonant frequency unchanged when capacitance is changed from C to 2C.
Hence, option B is the correct answer.
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