Does the current in an A.C. circuit lag, lead or remain in phase with the voltages of frequency v applied to the circuit when (i) `v = v_(r)` (ii) `v lt v_(r)` (iii) `v gt v_(r)` where `v_(r)` is the resonance frequency.

Explanation

(i) When `v = v_(r), X_(L) = X_(C)`.
The circuit is purely resistive, i.e., it is non-inductive. Therefore, current and voltage in the circuit are in the same phase.
(ii) When `v lt v_(r)` As `X_(L) = omega L = 2 pi v L` and
`X_(C ) = (1)/(omega C) = (1)/(1 pi v C)`
`:.` when v is small, `X_(L)` is small, `X_(C )` is large. The circuit is capacitance dominated. Therefore, current in the circuit leads the voltage by phase angle `phi`.
`X_(L)` becomes large and `X_(C )` becomes small. The circuit is inductance dominated. The current legs behind the voltage, by phase angle `phi`.