In series LCR circuit, the capacitance is changed from C to 4C. To keep the resonance frequency unchanged, the new inductance should be

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Solution

Q.
In series LCR circuit, the capacitance is changed from C to 4C. To keep the resonance frequency unchanged, the new inductance should be [2024]

1 reduced to L/4

2 increased by 2L

3 reduced by L/3

4 increased to 4L

Ans.
(1)

$ω^{'} = ω$

$\frac{1}{\sqrt{L^{'} C^{'}}} = \frac{1}{\sqrt{L C}} ∴ L^{'} C^{'} = L C$

$L^{'} (4 C) = L C$

$L^{'} = \frac{L}{4}$

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