Question

LC osillations are similar and analogous to the mechanical oscillations of a block attached to a spring. The electrical equivalent of the force constant of the spring is

• A. reciprocal of capacitive reactance
• B. capacitive reactance
• C. reciprocal of capacitance
• D. capacitance

Answer 1

The Correct Option is C

LC oscillations are analogous to the mechanical oscillations of a block attached to a spring. In a mechanical spring-block system, the force constant ($k$) determines the restoring force. We want to find the electrical equivalent of the force constant in an LC circuit.

In a spring-block system, the angular frequency ($\omega$) of oscillation is given by $\omega = \sqrt{\frac{k}{m}}$, where $k$ is the force constant and $m$ is the mass. 

In an LC circuit, the angular frequency is given by $\omega = \frac{1}{\sqrt{LC}}$ Thus $ \sqrt{\frac{k}{m}} = \frac{1}{\sqrt{LC}} \implies \frac{k}{m} = \frac{1}{LC} $ Since k can be analogous to $\frac{1}{C}$, the electrical equivalent of the force constant is the reciprocal of capacitance.

Capacitive reactance ($X_C$) is given by $\frac{1}{\omega C}$. Its reciprocal is $\omega C$, which is not analogous to the force constant. The reciprocal of capacitance is $\frac{1}{C}$.

The correct answer is (C) reciprocal of capacitance.