Question

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?

Answer 1

Here, `L = 2.0 H, C = 18 xx 10^(-6) F`,
`R = 10 k Omega = 10^(4) Omega, E_(v) = 20 V`
To maximum current,
`v = (1)/(2 pi sqrt(LC)) = (1)/(2 xx (22)/(7) xx sqrt(2 xx 18 xx 10^(-6))`
`v = (7 xx 10^(3))/(2 xx 22 xx 6) = 26.5 Hz`
At this frequency , `X_(L) = X_(C) , X = R`
`:. I_(0) = (E_(0))/(Z) = (E_(v) sqrt2)/(R )`
` = (20 xx 1.414)/(10^(4)) = 2.828 xx 10^(-3) A`
`= 2.828 mA`