JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Electromagnetic Induction

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In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes x times its initial resonant frequency

ω_{0}

. The value of x is:

(A) $1/4$ ✓ Correct
(B)16
(C) $1/16$
(D)4

Answer: (A)

Solution

The resonant frequency of an LC circuit is

ω_{0} = \frac{1}{L C}

. Replacing

L \to 2 L

and

C \to 8 C

multiplies the product under the root by

16

, so

ω = \frac{1}{16 L C} = \frac{1}{4} \cdot \frac{1}{L C} = \frac{ω _{0}}{4}

. The frequency falls to one-quarter of its original value, so

x = \frac{1}{4}

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Single correct option

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