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A series LCR circuit is connected to a 2...

A series LCR circuit is connected to a 220 V variable frequency supply. If L = 20 mH, `C = [(800)/(pi^(2))]muF` and `R = 110 Omega`,
(a) Find the frequency of the source for which the average power absorbed by the circuit is maximum.
(b) Calculate the value of maximum current amplitude.

Text Solution

Verified by Experts

Given, `L = 20 mH = 20 xx 10^(-3)H`
`C = (800)/(pi^(2)) = muF = (800)/(pi^(2)) xx 10^(-6)F`
`R = 110 Omega`
(a) `v = (1)/(2pi sqrt(LC))`
`= (1)/(2pi sqrt(20 xx 10^(-3) xx (800 xx 10^(-6)))/(pi^(2)))`
`= (1)/(2sqrt(16 xx 10^(-6))) = (1)/(8 xx 10^(-3))`
`= (1000)/(8) = 125 Hz`
(b) `I_(max) = (E)/(Z_(min)) = (E )/(R )`
`= (220)/(110) = 2A`
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