The currents at the terminals of a mesoscopic conductor are evaluated in the presence of slowly oscillating potentials applied to the contacts of the sample. The need to find a charge- and current-conserving solution to this dynamic current partition problem is emphasized. We present results for the electrochemical admittance describing the long-range Coulomb interaction in a Hartree approach. For multiply connected samples we discuss the symmetry of the admittance under the reversal of an Aharonov-Bohm flux.