In a series L - C - R circuit in which R = `3 Omega`, L = 25 m H and C = `800 mu F` a sinusoidal AC voltage of peak value 2250 V is applied. Find
(a) the frequency at which resonance occurs.
(b) the currnet in the circuit at resonant condition.

Explanation

Here , resistance, R `= 3 Omega`
Inductance, L = 25 mH = `25 xx 10^(-3) H`
Capacitance, C = `800 mu F = 800 xx 10^(-5) F`
Peak voltage, `E_(0) = 250 V`
(a) Frequency at which resonance occur
`v=(1)/(2pisqrt(LC))`
`=(1)/(2xx(22)/(7)xxsqrt((25xx10^(-3))xx(800xx10^(-6))))`
`=(1)/(28.26xx10^(-3))=(1000)/(28.26)`
= 35.38 Hz
(b) Impendance, `Z=sqrt(R^(2)+(X_(L)-X_(c))^(2))`
At resonance, `Z=sqrt(R^(2)+0)`
`("at resonance"X_(L)=X_(C))`
`therefore` Peak current in circuit = `(E_(0))/(Z)=(250)/(3)=83.33A`