Question

A series LCR circuit with `L = 0.12 H, C = 480 pF, R = 23 Omega` is connected to a 230 V variable frequency supply.
For which frequencies of the source is the power transferred to the circuit half power at resonant frequency ? What is the current amplitude at these frequencies ?

Answer 1

Inductance `L = 0.12 H`,
Capacitance `C = 480 nF = 480xx10^(-9)F`
Resistance `R = 23 Omega`
The rms value of voltage Vrms = 230 V
Power transferred to the circuit is half the power at resonant frequency.
`Delta omega=(R )/(2L)=(23)/(2xx0.12)=95.83` rad/s
`Delta V=(Delta W)/(2pi)=15.2Hz`
The frequencies at which power transferred is half
`V=V_(0)pm Delta V=663.48 pm 15.26`
So, frequencies are 448.3Hz and 678.2Hz, the maximum current
`I=(I_(0))/(sqrt(2))=(14.14)/(sqrt(2))=10A`