Suppose the frequency of the source in the above example can be varied (a) What is the frequency of the source at which resonance occurs ? (b) Calculate the impedance, the current and power dissipated at the resonant condition.

Explanation

(a) The frequency at which the resonance occurs is
`omega_(0)=(1)/sqrt(LC)=(1)/(sqrt(25.48xx10^(-3)xx796xx10^(-6)))`
=222.1rad/s
`v_(r)=(omega_(0))/(2pi)=(221.1)/(2xx3.14)Hz=35.4Hz`
(b) The impedance Z at resonant condition is equal to the resistance:
Z=R=`3Omega`
The rms current at resonance is
`=(V)/(Z)=(V)/(R)=((283)/(sqrt(2)))(1)/(3)=66.7A`
The power dissipated at resonance is
`P=I^(2)xxR=(66.7)^(2)xx3=13.35kW`
You can see that in the present case, power dissipated at resonance is more than the power dissipated in Example 7.8.