Question

Figure shows a series LCR circuit connected to a variable frequency 230 V source. `L = 5.0 H, C = 80 mu F, R = 40 Omega`.

Obtain the impedance of the circuit and the amplitude of current at the resonanting frequency.

Answer 1

Given, the rms value of voltage `V_("ims")=230 V`
Inductance L = 5H
Capacitance `C = 80 mu f = 80xx10^(-6)F`
Resistance `R = 40 Omega`
At the resonant frequency, `X_(L)=X_(C )`
So, impedance of the circuit Z = R.
`therefore` Impedance `Z = 40 Omega`
The rms value of current in the circuit
`I_("rms")=(V_("rms"))/(Z)=(230)/(40)=5.75 A`
Amplitude of current `I_(0)=I_("rms")sqrt(2)`
`= 5.75xx sqrt(2)`
`= 8.13 A`