In an L-C-R series circuit, R = 500`Omega` L = 10 ml of an ideal inductor and C = 20 `muF`, thes components connected to A.C. source of 230 V 50Hz. The power in the circuit will be .....

Options

A. 98 W
B. 89 W
C. 980 W
D. 98 mW

Answer

A

Explanation

`|Z|=sqrt(R^2+(X_L-X_C)^2)`
`=sqrt((50)^2+(100pixx10^(-2)-1/(100pixx20xx10^(-6)))^2`
`=sqrt(2500+(3.14-1000/(2pi))^2)`
`=sqrt(2500+(3.14-159.2)^2)`
`=sqrt(2500+(-156)^2)`
`=sqrt26836`
`therefore` |Z|=163.8
`therefore |Z| approx 164 Omega`
Now power `P=I_"rms"^2R`
where `I_"rms" = V_"rms"/"|Z|" = 230/164`
`therefore I_"rms"`=1.4 A
`therefore P=(1.4)^2 xx 50 = 1.96 xx50`
`therefore` P=98 W