A source of alternating emf of 220 V-50 Hz is connected in series with a resitance of `200 Omega` an inductance of 100 mH and a capacitance of `30 mu F` does the current lead or lag the voltage and by what angle ?

Explanation

Given `V_(rms ) =200 v, f= 50 Hz , R = 200 Omega`
` L=100 xx10 ^(-3) = 0.1 H,C `
`=30 xx10 ^(-6) F=3 xx 10 ^(-5) F `
Interactive rectance `X_(L )= 2 pi fL`
` i.e., X_(L ) 2xx3.142 xx50 xx0.1 Omega `
`i.e., X_(L ) = 31.42 Omega `
Capacitive rectance `X_(C) = (1)/(2 pi fC )`

`i.e., X_(C) =(1)/(2xx3.142xx50xx3xx10 ^(-5))`
`i.e., X_(C ) =(1000) /( 9.426 )= 106 .08 Omega `
Rectance of the circult `X_(L ) - X_(c) = 31.42 -106.08`
`i.e., X_(L ) - X_(C) =- 74.6 Omega `
` wkt tan phi =(X_(L)-X_(C))/(R )`
i.e., ` tan phi = -74.66 )/(200 )=0.3733 `
Hence ` f=-20 ^@ 30 ^1`
i.e., the current leads the voltage by`20 ^@30 ^1`