In inductively coupled radio frequency (RF) plasmas a mode transition between a low-power mode with dominant capacitive coupling (E-mode) and a high-power mode with dominant inductive coupling (H-mode) has been frequently reported in the literature. We investigate this transition, which results in an increase of the light emission by up to two orders of magnitude. Furthermore we observe a hysteresis of this mode transition. Two major aspects of the transition are addressed in this paper. First we propose an explanation for the discontinuous character of the mode transition. The analysis is based on a simple, electrodynamic model of the inductive discharge. This analysis shows that a certain minimum maintenance RF coil current is required for the operation of an inductive discharge and that the skin effect of the RF field is essential for stable discharge operation. This point is supported by experimental observations. In the second part of the paper we present a simple, self-consistent analytic description of the discharge, which enables us to calculate the minimum maintenance RF coil current. The theoretical results are found to be in reasonable agreement with the measured minimum maintenance coil currents.