A

In a series AC circuit made up of an inductor (L), capacitor (C), and resistor (R), the phase angle (\phi) between the total voltage (e.m.f.) and the current can vary based on the impedance (Z) of the circuit. The general relationship is given by:
\[ \tan(\phi) = \frac{X_L - X_C}{R} \]
where \(X_L\) is the inductive reactance and \(X_C\) is the capacitive reactance.

In conditions where the circuit is either resistive or predominantly inductive/capacitive, the phase angle can range from 0 to \(\frac{\pi}{2}\) radians (90 degrees). Specifically:
- When \(R > X_L - X_C\), the phase angle is less than 90 degrees.
- When the circuit is purely resistive (R = 0), the phase angle is 0.
- When the circuit becomes purely capacitive (R = 0), the angle approaches 90 degrees.

Therefore, the phase angle between e.m.f. and current in a series AC circuit can reasonably be said to vary from 0 to \(\frac{\pi}{2}\). Hence, the correct option is A.