Question

In an LCR series resonance circuit driven by the alternating voltage \( V = V_0 \sin \omega t \), inductance \( L = 1 \, \mu H \), capacitance \( C = 1 \, \mu F \) and resistance \( R = 1 \, k\Omega \). The resonant angular frequency (in rad/s) is:

• A. \( 10^6 \)
• B. \( 10^{-6} \)
• C. \( 10^{12} \)
• D. \( 10^{16} \)
• E. \( 10^{10} \)

Hint:

The resonant frequency in an LCR circuit is determined by the inductance and capacitance. Remember, \( \omega_0 = \frac{1}{\sqrt{LC}} \).

Answer 1

The Correct Option is A

The resonant angular frequency \( \omega_0 \) of an LCR circuit is given by the formula: \[ \omega_0 = \frac{1}{\sqrt{LC}} \] Substitute the given values: - \( L = 1 \, \mu H = 10^{-6} \, H \), - \( C = 1 \, \mu F = 10^{-6} \, F \). Thus: \[ \omega_0 = \frac{1}{\sqrt{(10^{-6})(10^{-6})}} = \frac{1}{\sqrt{10^{-12}}} = 10^6 \, {rad/s} \] Hence, the correct answer is (A).