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Question

Answer in brief:
What is the natural frequency of the LC circuit? What is the reactance of this circuit at this frequency?


Solution

$$X_{L}=-X_{C}$$
$$\Rightarrow \omega L=\dfrac{1}{\omega C}$$
$$\omega^{2}LC=1$$

$$\omega=\dfrac{1}{\sqrt{2C}}$$

$$\omega=2\pi f\Rightarrow f=\dfrac{\omega}{2}\pi =\dfrac{1}{2\pi \sqrt{LC}}$$

Total reactance $$=X_{L}+X_{C}$$
$$=-X_{C}+X_{C}$$
$$=0$$
$$V=\dfrac{1}{2\pi \sqrt{LC}}$$
Reactance of the circuit at this frequency is zero.

Physics
NCERT
Standard XII

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