Question

A series circuit contains a 100.0-Ω resistor, a 0.450-H inductor, a 0.360-µF capacitor, and a time-varying source of emf providing 30.0 V.

(a) What is the resonant angular frequency of the circuit?
(b) What current will flow through the circuit at the resonant frequency?

Answer 1

Answer:

A) The resonance angular frequency in an L-R-C circuit is

$\omega_0 = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{0.45\times0.36\times 10^{-6}}}\\\omega_0 = 2.48\times10^3 rad/s$

B) The current can be found by calculating the impedance of the system.

$Z = \sqrt{R^2 + (X_L - X_C)^2} = R$

Since $X_L = X_C$ at resonance.

So, $I = V/Z = V/R = 30 / 100 = 0.3A$