A 200 V varialbe frequency a.c. source is connected to a series combination the `L= 5H , C = 80 mu F and R = 40 Omega`. Calculate the angular frequency of the soucre to get maximum current in the cicuit, the current amplitude at resonance and power dissipated in the circuit.

Explanation

`L = 5H, C= 80 muF = 80 xx 10^(-6) F`
`R =40Omega`
(a) Resonant frequency `=v_0=?`
`v_0=1/(2pisqrt(LC))`
`v_0 = 1/(2xx3.14sqrt(5xx80xx10^(-6))`
`1/(6.28xx20xx10^(-3))`
`= 7.96Hz`
(b) Impedance `Z = sqrt(R^2+(X_L-X_C)^2)`
But at resonance , `X_L = X_C`
`Z=sqrt(R^2)=R`
`Z = 40Omega`
`E_(rms) = 230 V` (Given)
(c) `I_v = I_(rms)=E_(rms)/Z`
`=230/40 = 5.75A`
Amplitude of current at resonance `=I_0 = sqrt2I_v`
`= 1.414 xx5.75`
`= 8.131A`