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An L-C-R series circuit with 100Omega re...

An `L-C-R` series circuit with `100Omega` resistance is connected to an `AC` source of `200V` and angular frequency `300rad//s`. When only the capacitance is removed, the current lags behind the voltage by `60^@`. When only the inductance is removed the current leads the voltage by `60^@`. Calculate the current and the power dissipated in the `L-C-R` circuit

Text Solution

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If first case `tan 60^(@)=(X_(L))/R=(omega L)/R`
or `sqrt(3)=(300L)/100`
`:.L=0.58H`
In second case, `tan 60^(@)=(X_(C))/R=1/(omega CR)`
or `sqrt(3)=1/(300Cxx100)`
`:.C=19.2mu F`
The impedance of the circuit is
`Z=sqrt(R^(2)+(omega L-1/(omegaC))^(2))`
`=sqrt(100^(2)+(300xx0.58-1/(300xx19.2xx10^(-6)))^(2))`
`=100Omega`
Current `i=V/Z=200/100=2A`
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