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: Apply the formula for LC circuit oscillation frequency The frequency \( f \) of an LC circuit is calculated using the formula: \[f = \frac{1}{2\pi \sqrt{LC}}\] where \( L \) represents inductance, \( C \) represents capacitance, and \( f \) is the oscillation frequency. Step 2: Input the provided values The given values are: - Inductance \( L = 2 \, \text{H} \) - Capacitance \( C = 4 \, \mu\text{F} = 4 \times 10^{-6} \, \text{F} \) 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: The calculated oscillation frequency for the LC circuit is approximately \( 56.3 \, \text{Hz} \). This corresponds to option (2).