In an AC circuit, the current leads the voltage by π/2. The circuit is ________.

The correct option is purely capacitive.

To understand why this is the case, we can analyze the relationship between voltage and current in different types of basic AC circuits containing resistors, inductors, or capacitors.

1. Purely Resistive Circuit:
In a circuit containing only resistance, the alternating current and alternating voltage are in phase with each other. This means the phase angle between them is zero, and both reach their maximum and minimum values at the same time.

2. Purely Inductive Circuit:
In a circuit containing only an inductor, the alternating voltage leads the alternating current by a phase angle of π/2 radians (or 90 degrees). In other words, the current lags the voltage by π/2.

3. Purely Capacitive Circuit:
When an alternating voltage is applied across a capacitor, the capacitor continuously charges and discharges as the voltage alternates. The current flowing through the circuit is proportional to the rate of change of voltage. Specifically, if the applied voltage is given by the equation:

$v\left(t\right)=V_m\sin \left(\omega t\right)$

Then, the resulting current through the purely capacitive circuit is represented by:

$i\left(t\right)=I_m\sin (\omega t+\frac{\pi }{2})$

Comparing these two equations, we see that the phase angle of the current is greater than that of the voltage by π/2. This demonstrates that the current leads the voltage by π/2. Therefore, the circuit is purely capacitive.