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 sourc

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 sourc

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 ?

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

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`