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 xx 10^(-6) F=3 xx10^(-5) F`
Interactive rectance `X_(1) =2pi fL`
i.e `X_(L) =2 xxx3.142 xx50 xx0.1 omega`
i.e `X_(L) =31.42 omega`
capacitive rectance `X_(c )=(1)/(2pifc)`
Reactence of the circuit `X_(L) -X_(C )=31.42 -106.08`
i.e `X_(L)-X_(c )=-74.6 omega`
wkt `tan theta =(X_(L)-X_(c))/(R )`
i.e `tan theta =(-74.66)/(200)=0.3733`
hence `f=-20^(@)30^(1)`
i.e the current leads the voltage by `20^(@) 30^(1)`