Fig. show a series LCR circuit with `L = 0.1 H l, X_(C ) = 14 Omega` and `R = 12 Omega` connected to a 50 Hz, 200 V source. Calculate
(i) current in the circuit and
(ii) phase angle between current and voltage.
Take `pi = 3`

Explanation

Here, `R = 12 Omega, X_(C ) = 14 Omega, L = 0.1 H`
`E_(v) = 200 V, v = 50 Hz`
`X_(L) = omega L = 2 pi v L = 2 xx 3 xx 50 xx 0.1 = 30 Omega`
`Z = sqrt(R^(2) + (X_(L) - X_(C))^(2)) = sqrt(12^(2) + (30 - 14)^(2)) = 20 Omega`
`I_(v) = (E_(v))/(Z) = (200)/(20) = 10 A`
As `X_(L) gt X_(C )`, current lags behind the applied voltage by phase angle `phi`, where
`tan phi = (X_(L) = X_(C ))/(R ) = (30 - 14)/(12) = 1.3333`
`phi = tan^(-1) (1.3333) = 53.1^(@)`