In a large magnetized laboratory plasma(n≃1012cm−3,kTe⩾1eV,B0⩾10G, 1 m×2.5 m), the transient processes of switch-on currents to electrodes are investigated experimentally. The current rise time lies between the ion and electron cyclotron periods (electron magnetohydrodynamics). The initial current scales linearly with applied voltage and isnotlimited by the electron saturation current of the positive electrode, but by the ion saturation current of the return electrode. The collection of electrons in the flux tube of the positive electrode gives rise to a space charge electric field, which expels the unmagnetized ions, erodes the density, and disrupts the current. Repeated current oscillations arise from a feedback between current, density, and potential oscillations. The dependence of the transient and unstable electrode currents on externally variable parameters is investigated in the present paper. A companion paper [Urrutia and Stenzel, Phys. Plasmas4, 36 (1997)] presentsin situmeasurements of plasma currents, plasma parameters, and microinstabilities. These results are relevant to the physics of pulsed Langmuir probes, current collection from tethered electrodes in space, and plasma erosion switches. ©1997 American Institute of Physics.