Question

A series resonant ac circuit contains a capacitance \(10^4\) F and an inductor of \(10^-4\) H. The frequency of electrical oscillations will be

• A. \(\frac{{10^5}}{{2\pi}}\)Hz
• B. \(10^3\) Hz
• C. \(\frac{{10}}{{2\pi}}\) Hz
• D. 10 Hz

Answer 1

The Correct Option is A

The resonance frequency (\( v \)) of an LC circuit is given by the formula:

\( v = \frac{1}{2 \pi \sqrt{L C}}\)

Substituting the values for the capacitance (\( C = 10^{-4} \)) and inductance (\( L = 10^{-6} \)):

\( v = \frac{1}{2 \pi \sqrt{10^{-6} \times 10^{-4}}} = \frac{1}{2 \pi \sqrt{10^{-10}}}\)

\(v = \frac{10^5}{2 \pi} \, \text{Hz}\)

Therefore, the resonance frequency of the circuit is: \( \frac{10^5}{2 \pi} \, \text{Hz} \).