Question

A series a,c circuit consists of an inductor and a capacitor. The inductance and capacitance are respectively 1 henry and 25 Fμ. If the current is maximum in the circuit then the angular frequently will be

• A. 50 rad/s
• B. 100 rad/s
• C. \(\frac{200}{2\pi}\) rad/s
• D. 200 rad/s

Answer 1

The Correct Option is D

To find the angular frequency at which the current is maximum in a series a.c. circuit containing an inductor and a capacitor, we need to determine the resonant frequency. The resonant frequency in an LC circuit is given by the formula: \(\omega_0 = \frac{1}{\sqrt{LC}}\), where \(L\) is the inductance, and \(C\) is the capacitance.

Substituting the given values \(L = 1\, \text{H}\) and \(C = 25\, \mu\text{F} = 25 \times 10^{-6}\, \text{F}\), we have:

\[\omega_0 = \frac{1}{\sqrt{1 \times 25 \times 10^{-6}}}\]

Simplifying inside the square root gives:

\[\omega_0 = \frac{1}{\sqrt{25 \times 10^{-6}}} = \frac{1}{5 \times 10^{-3}} = \frac{1}{0.005}\]

Continuing with the calculation:

\[\omega_0 = \frac{1}{0.005} = 200\, \text{rad/s}\]

Therefore, the angular frequency at which the current is maximum in the circuit is 200 rad/s.