Question

In an LC circuit, the inductance \( L \) is \( 2 \, \text{H} \) and the capacitance \( C \) is \( 4 \, \mu\text{F} \). What is the frequency of oscillation of the circuit?

• A. \( 100 \, \text{Hz} \)
• B. \( 50 \, \text{Hz} \)
• C. \( 25 \, \text{Hz} \)
• D. \( 200 \, \text{Hz} \)

Hint:

Remember: The frequency of an LC circuit depends on both the inductance and capacitance. A higher inductance or capacitance leads to a lower frequency of oscillation.

Answer 1

The Correct Option is B

Step 1: Use the formula for the frequency of oscillation in an LC circuit The frequency \( f \) of an LC circuit is given by the formula: \[ f = \frac{1}{2\pi \sqrt{LC}} \] where: - \( L \) is the inductance, - \( C \) is the capacitance, - \( f \) is the frequency of oscillation. Step 2: Substitute the given values Given: - Inductance \( L = 2 \, \text{H} \), - Capacitance \( C = 4 \, \mu\text{F} = 4 \times 10^{-6} \, \text{F} \). Now, substitute these values into the formula: \[ f = \frac{1}{2\pi \sqrt{2 \times 4 \times 10^{-6}}} \] \[ f = \frac{1}{2\pi \sqrt{8 \times 10^{-6}}} \] \[ f = \frac{1}{2\pi \times 2.83 \times 10^{-3}} = \frac{1}{1.78 \times 10^{-2}} = 56.3 \, \text{Hz} \] Answer: Therefore, the frequency of oscillation of the LC circuit is approximately \( 50 \, \text{Hz} \). So, the correct answer is option (2).