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

`X_L=2pivL=31.4pi`
`X_C=1//2pivC=106.1 Omega`
Since `X_C gt X_L` currents leads the voltage or voltage lags the current
`tan phi=(X_C-X_L)/R=0.3734`
`phi=20.5^@`
(Since `phi` is positive , current leads the voltage)
Given , `V_(rms)`=200 V, f=50 Hz , R=200 W
`L=100xx10^(-3)` = 0.1 H, `C=30xx10^(-6) F=3xx10^(-5)` F

Interactive reactance `X_L=2pifL`
i.e., `X_L=2xx3.142xx50xx0.1W`
i.e., `X_L`=31.42 W
Capacitance reactance , `X_C=1/(2pifC)`
i.e., `X_C=1/(2xx3.1742xx50xx3xx10^(-5))`
i.e., `X_C=1000/9.426=106.08Omega`
Reactance of the circuit , `X_L-X_C` = 31.42-106.08
i.e., `X_L-X_C`=-74.6 W
`rArr tan phi = (X_L-X_C)/R`
i.e., `tan phi =(-74.66)/200`=0.3733
Hence `f=-20^@ 30.`
i.e., the current leads the voltage by `20^@30.`.