An inductance of `2.0 H`, a capacitance of `18 muF` and a resistance of `10 kOmega` are connected to an AC source of `20 V` with adjustable frequency. (a) What frequency should be chosen to maximise the current in the circuit? (b) What is the value of this maximum current?

Explanation

(a) For current to be maximum in a circuit
`X_L = X_C` (Resonant Condition)
implies `omegaL = 1/(omegaC)`
implies `omega^2 = (1)/(LC) = (1)/(2 xx 18 xx 10^-6)`
`=10^6/36`
implies ` omega = 10^3/6 implies 2pif= 10^3/6`
implies `f= (1000)/(6 xx 2pi) = 26.539 Hz`
`=27 Hz`.
(b) Maximum current
`=E/R = (20)/(10 xx 10)^3`
`=(20A)/10^3 = 2mA`
(Inresonance condition)