First slide

L - C Oscillations

Question

In an LCR ac circuit, the resistance and reactances $R, X_{C} a n d X_{L}$ are in the ratio 1 : 3 : 4 .The frequency of ac is $f_{0}$ . The resonant frequency of the circuit will be

Easy

A

$\frac{3}{4} f_{0}$
B

$\sqrt{\frac{3}{4}} f_{0}$
C

$\sqrt{\frac{4}{3}} f_{0}$
D

$f_{0}$

Solution

$\frac{X_{L}}{X_{C}} = ω^{2} (L C) = \frac{4}{3}$ , $f_{0} = \frac{1}{2 π} \sqrt{\frac{4}{3 L C}}$ ,
now $X_{L} = X_{C} \Rightarrow ω^{2} = \frac{1}{L C} \Rightarrow f_{r} = \frac{1}{2 π} \frac{1}{\sqrt{L C}}$

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