Equivalent circuit (series capacitor on inductive pickup)
Since the voltage source for the circuit is AC, the capacitor will exhibit reactance. This reactance is in series with the source so it can have an effect on the output voltage depending on the load placed at the output.

The reactance of the capacitor is frequency dependent so if the frequency range of the AC signal is large enough the capacitor, along with any series resistance, acts as a filter. That probably will not be the case in your application.

The capacitor also blocks any DC component that might be present with the AC signal. This is a common decoupling technique to yield only the desired AC signal.