A LC circuit is in the state of resonance. If | vedclass

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Question

(A) The resonant frequency of an $LC$ circuit is given by the formula: $
u_0 = \frac{1}{2\pi\sqrt{LC}}$.Given values are $L = 0.25 \ H$ and $C = 0.1

Vedclass · Accepted Answer

$1007$

Vedclass · Answer

(A) The resonant frequency of an $LC$ circuit is given by the formula: $
u_0 = \frac{1}{2\pi\sqrt{LC}}$.Given values are $L = 0.25 \ H$ and $C = 0.1 	imes 10^{-6} \ F$.Substituting these values into the formula:$
u_0 = \frac{1}{2 	imes 3.14159 	imes \sqrt{0.25 	imes 0.1 	imes 10^{-6}}}$$
u_0 = \frac{1}{6.28318 	imes \sqrt{0.025 	imes 10^{-6}}}$$
u_0 = \frac{1}{6.28318 	imes \sqrt{25 	imes 10^{-9}}}$$
u_0 = \frac{1}{6.28318 	imes 1.5811 	imes 10^{-4}}$$
u_0 = \frac{10^4}{6.28318 	imes 0.15811} \approx \frac{10000}{9.934} \approx 1006.6 \ Hz$.Rounding to the nearest integer,we get $1007 \ Hz$.

$A$ $LC$ circuit is in the state of resonance. If $C = 0.1 \mu F$ and $L = 0.25 \ H$. Neglecting the ohmic resistance of the circuit,what is the frequency of oscillations in $Hz$?

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