Question

A charged 30 $\mu$F capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?

• A. 11 rad/s
• B. 1100 rad/s
• C. 110 rad/s
• D. 11000 rad/s

Hint:

To solve square roots with powers of 10 easily, always adjust the decimal so the power of 10 is an \textbf{even} number.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In an LC circuit, energy oscillates between the electric field of the capacitor and the magnetic field of the inductor at a specific resonant frequency.
Step 2: Formula Application:
The angular frequency $\omega$ is given by $\omega = \frac{1}{\sqrt{LC}}$.
Step 3: Explanation:
Given: $C = 30 \times 10^{-6}$ F, $L = 27 \times 10^{-3}$ H. $$\omega = \frac{1}{\sqrt{27 \times 10^{-3} \times 30 \times 10^{-6}}} = \frac{1}{\sqrt{810 \times 10^{-9}}} = \frac{1}{\sqrt{81 \times 10^{-8}}}$$ $$\omega = \frac{1}{9 \times 10^{-4}} = \frac{10000}{9} \approx 1111.11 \text{ rad/s}$$
Step 4: Final Answer:
The angular frequency is approximately 1100 rad/s.