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

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

`\omega_0 = (1)/(√(LC)) = \frac{1}{\sqrt{0.45*0.36* 10^(-6)}}\\\omega_0 = 2.48*10^3 rad/s`

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

`Z = √(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`