Question

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

• A. 100 Hz
• B. 50 Hz
• C. 25 Hz
• D. 200 Hz

Hint:

Remember: The frequency of oscillation for an LC circuit depends on the values of inductance \( L \) and capacitance \( C \). Use the formula \( f = \frac{1}{2\pi \sqrt{LC}} \) to calculate the frequency.

Answer 1

The Correct Option is B

Given:Inductance, \( L = 2 \, \text{H} \) 
Capacitance, \( C = 4 \, \mu\text{F} = 4 \times 10^{-6} \, \text{F} \)

Step 1: Formula for Frequency of Oscillation The frequency \( f \) of oscillation for an LC circuit is given by the formula: \[ f = \frac{1}{2\pi \sqrt{LC}} \] where: - \( L \) is the inductance, - \( C \) is the capacitance. 

Step 2: Substitute the given values Substitute the given values into the formula: \[ f = \frac{1}{2\pi \sqrt{(2 \, \text{H})(4 \times 10^{-6} \, \text{F})}} \] \[ f = \frac{1}{2\pi \sqrt{8 \times 10^{-6}}} \] \[ f = \frac{1}{2\pi \times 2.828 \times 10^{-3}} \] \[ f \approx \frac{1}{1.777 \times 10^{-2}} \] \[ f \approx 56.3 \, \text{Hz} \] 

Step 3: Conclusion The frequency of oscillation is approximately \( 50 \, \text{Hz} \) (rounded to the nearest option). 

Answer: The correct answer is option (b): 50 Hz.