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 power dissipated in the `L-C-R` circuit

Options

A. `50 W`
B. `100 W`
C. `200 W`
D. `400 W`

Answer

D

Explanation

`tan phi=(X_(L))/R=(X_(C))/Rimplies tan 60^(@)=(X_(L))/R=(X_(C))/R`
`implies X_(L)=X_(C)=sqrt(3)R`
i.e., `Z=sqrt(R^(2)+(X_(L)-X_(C))^(2))=R`
So average power `P=(V^(2))/R=(200xx200)/100=400W`