Question

How does the sign of the phase angle `phi`, by which the supply voltage leads the current in an LCR series circuit, change as the supply frequency is gradually increased from very low to very high values.

Answer 1

The phase angle `phi` by which voltage leads the current in LCR series circuit where X_L > X_C.

`tan phi = (X_L - X_C)/R = (2pivL - 1/(2pivC))/R`

If v is small X_C > X_L so `[2πvL - 1/(2πvC)]` is negative, so tan `phi < 0`.

For v is large, X_L > X_C

So X_L = X_C is positive to `tan phi > 0`

For X_L = X_C i.e. at resonant frequency

X_L – X_C = 0 so `tan phi` = 0.

So phase angle in series LCR ac circuit will change from a negative to zero and then zero to positive value.