A coil is series with a `20muF` capacitor across a `230V, 50Hz` supply. The current taken by the circuit is `8A` and the power consumed is `200W.` Calculate the inductance of the coil if the current in the circuit is
(a) leading
(b) lagging

Answer

A, B, D

Explanation

`P=V_("rms")i_("rms")cosphi`
or `200=230xx8xxcosphi`
`:. cosphi=0.108`
or `phi=83.8^@`
Further, `P=i_("rms")^2R`
`:. R=P/i_("rms")^2=200/((8)^2)=3.125Omega`
(a) `tan phi=(X_C-X_L)/R`
`:. 1/(2pifC)-(2pifL)=Rtanphi`
`:. 1/((2pif)^2C)-(Rtanphi)/(2pif)`
`=1/((2pixx50)^2xx20xx10^-6)-(3125tan83.8^@)/(2pixx50)`
(b) `tanphi=(X_L-X_C)/R`
or `2pifL-1/((2pifC))=Rtan phi`
`L=1/((2pif)^2C)+(Rtanphi)/((2pif))`
`1/((2xxpixx50)^2xx20xx10^-6)+(3.125tan83.8^@)/((2pixx50))`
`=0.597H`.