Question

A 0.1 H inductor, a 25 × 10\(^{-6}\) F capacitor, and a 15 Ω resistor are connected in series to a 120 V, 50 Hz AC source. Calculate the resonant frequency.

Hint:

Resonant frequency depends only on \( L \) and \( C \); use \( f_0 = \frac{1}{2\pi \sqrt{L C}} \).

Answer 1

Resonant frequency of an LCR series circuit: \[ f_0 = \frac{1}{2\pi \sqrt{L C}}, \] where \( L = 0.1 \, \text{H} \), \( C = 25 \times 10^{-6} \, \text{F} \).
\[ L C = 0.1 \times 25 \times 10^{-6} = 2.5 \times 10^{-6}. \] \[ \sqrt{L C} = \sqrt{2.5 \times 10^{-6}} = \sqrt{2.5} \times 10^{-3} \approx 1.5811 \times 10^{-3}. \] \[ f_0 = \frac{1}{2 \pi \times 1.5811 \times 10^{-3}} \approx \frac{1}{9.935 \times 10^{-3}} \approx 100.65 \, \text{Hz}. \] Answer: \( 100.65 \, \text{Hz} \).