Question

In an rlc ac circuit, the values of the inductance and capacitance are both doubled. as a result of this change, the resonance frequency of the circuit is?

Answer 1

f = 1 / 4 *  Π *    $\sqrt{L * C}$

The resonant frequency becomes half.

In resonance, $X_{L}$= $X_{C}$ -------- (1)

Where, $X_{L}$,  $X_{C}$ are the inductive and capacitive reactance of the RLC AC circuit.

We know that,

$X_{L}$ =  2 * Π * f  * L

$X_{C}$ = 1 / 2 * Π * f * C

Where f is the frequency.

substituting the values of inductive and capacitive reactance in equation (1).

2 * Π * f  * L =  1 / 2 * Π * f * C

On solving we get

$f^{2}$ = 1 / 4 * Π *  Π *  L * C

Therefore, f = 1 / 2 *  Π * $\sqrt{L * C}$

As values of L and C are doubled.

L = 2 * L

C = 2 * C

f = 1 / 2 * Π *  $\sqrt{4 * L * C}$

f = 1 / 4 *  Π *    $\sqrt{L * C}$

Hence, the resonant frequency becomes half.

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