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 ω0. The value of x is:

Question

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 ω0. The value of x is: (A) 1 / 4 (B) 4 (C) 16 (D) 1/16

Tardigrade Admin · Accepted Answer

The resonance frequency of LC oscillations circuit is ω0=(1/√ LC ) L arrow 2 L C arrow 8 C ω=(1/√2 L × 8 C )=(1/4 √ LC ) ω=(ω0/4) So x=(1/4)

Q. 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:

$1/4$

4

16

1/16

The resonance frequency of LC oscillations circuit is
$ω_{0} = \frac{1}{L C}$
$L \to 2 L$
$C \to 8 C$
$ω = \frac{1}{2 L \times 8 C} = \frac{1}{4 L C}$
$ω = \frac{ω _{0}}{4}$
So $x = \frac{1}{4}$

Q. 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 ω0​. The value of x is:

1/4

4

16

1/16

The resonance frequency of LC oscillations circuit is ω0​=LC​1​ L→2L C→8C ω=2L×8C​1​=4LC​1​ ω=4ω0​​ So x=41​

Q. 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:

$1/4$

The resonance frequency of LC oscillations circuit is
$ω_{0} = \frac{1}{L C}$
$L \to 2 L$
$C \to 8 C$
$ω = \frac{1}{2 L \times 8 C} = \frac{1}{4 L C}$
$ω = \frac{ω _{0}}{4}$
So $x = \frac{1}{4}$