Quantum effects in a small-capacitance Josephson junction coupled capacitively to an external circuit are investigated. Capacitive coupling permits one to control the charge on the junction and to hold the junction in an equilibrium state. The equilibrium state is characterized by a persistent voltage drop without an accompanying dc current. The persistent voltage is a periodic function of the control charge with period 2e if Cooper pairs only are present and with period e if quasiparticles are included. In the capacitively coupled junction, Bloch oscillations are induced by increasing the control charge linearly in time. The presence of a persistent voltage drop is reflected in the small-signal impedance of the circuit which describes the response of the junction to an oscillating control charge superimposed on a static control charge. The impedance reveals features which seem closely related to experimental observations by Lambe and Jaklevic [Phys. Rev. Lett. 22, 1371 (1969)] on a normal array of capacitively coupled junctions. © 1987 The American Physical Society.