Alternating Current

JEE Main level, single correct, medium

86 of 190

Question 86 of 190

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes xx times its initial resonant frequency ω0{\omega }_{0}. The value of xx is:

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Answer: (A) 14\dfrac{1}{4}

Resonance frequency of an LC oscillations circuit is stated as
ω0=1LC{\omega }_{0}=\dfrac{1}{\sqrt{LC}}, here, LandCLandC represents inductance and capacitance of circuit.
Now, when inductance and capacitance changes, i.e., L′=2L{L}^{'}=2L and C′=8C{C}^{'}=8C
Then, resonant frequency is ω=12L×8C=14LC\omega =\dfrac{1}{\sqrt{2L\times 8C}}=\dfrac{1}{4\sqrt{LC}}
⇒ω=ω04\Rightarrow \omega =\dfrac{{\omega }_{0}}{4}
Thus, the value of x=14x=\dfrac{1}{4}.

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