Auxinput 10-27-2016
... the primary driver of the audio signal is the main signal wire - as it is the only one connected to the input/output legs of the operation amplifier circuits.
To clarify further, in the case of an unbalanced input the active stage receiving the signal will respond to the difference in voltage between what it receives on its input signal connection and its own circuit ground. That stage will have a certain input impedance, which represents the impedance between its input signal connection and its own circuit ground. Any current flowing into that stage via the signal connection can be thought of as flowing through that input impedance to that circuit ground, and from there back to the source of the signal, via whatever path(s) is or are available. If no return path is available, no signal current will flow, and the input will "float," with unpredictable and perhaps damaging results if the signal line is connected by itself.
So the signal current and the total of the return currents that flow through whatever return paths exist will always be equal, while alternating in direction on each half-cycle of a given frequency. Just as the currents in the hot and neutral conductors of AC wiring are equal and opposite.
Similarly, the output stage of the component providing the signal can be thought of as an ideal voltage source (meaning a voltage source having zero output impedance) in series with some output impedance. And the current it provides can be thought of as flowing through that voltage source and that output impedance, between the output signal connection and the circuit ground of that stage. And if the only return path that is present between it and the component receiving the signal is via the ground sleeve of the RCA output connector, equal and opposite currents will be caused by that voltage source to flow through the center pin and the ground sleeve of that connector. And correspondingly through the cable. Although the currents may be unequal if other voltage sources contribute to what flows through that ground connection.
Best regards,
-- Al