An LCR series circuit with `L = 100 mH, C = 100 muF, R = 120 Omega` is connected to an `AC` source of `emf epsilon = (30 V) sin (100s^(-1))t`. Find the impedane, the peak current and the resonant frequency of the circuit.

Explanation

The reatance of the circuit is
`X = (1)/(omega C)-omegaL`
`= 1/((100 s^(-1) (100 xx 10^(-6) F)) - (100 s^(-1)) xx (100 xx 10^(-3) H)`
`= 100 Omega - 10 Omega = 90 Omega`.
The resistance is `R = 120 Omega`.
The impedance is
`Z = sqrt(R^2 + X^2)`
`= sqrt((120 Omega)^2 + (90 Omega)^@) = 150 Omega`.
The peak current is
`i_0 = epsilon_0/Z = (30 V)/(150 Omega) = 0.2 A`.
The resonant frequency of the circuit is
`v = 1/(2pi) sqrt(1/(LC))`
`= 1/(2pi) sqrt(1/((100 xx 10^(-3) H) (100 xx 10^(-6) F))`
`= 50 Hz`.