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

Here `omega = 100 rad s^(-1)`
`X_L = omega L = (100 rad s^(1)) xx (100 xx 10^(-3) H) = 10 Omega`
`X_C = (1)/(omega C) = (1)/((100 rad s^(-1)) xx (100 xx 10^(-6) F) ) = 100 Omega`
Now ,
` Z = sqrt(R^2 + (X_L - X_C)^2) = sqrt((120)^2 +(10 - 100)^2)`
` Z = sqrt((120)^2 + (90)^2) = 150 Omega`
`I_0 = (epsi_0)/(Z)= (30V)/(150 Omega ) = 0.2 A`