Electrical discharges at the ignition limit caused by opening contacts, which can generate ignitions in hydrogen/air mixtures with constant currents lower than 100 mA and at a maximum voltage of 30 V, have not been adequately described in scientific publications to date. In this article, the investigations and results of this critical range near the ignition limit are presented. Even constant currents greater than 40 mA can lead to an ignition of the hydrogen/air mixture. The discharges occurring in this case are characterized by processes that take place before the relevant discharge (so-called preliminary processes) and by slow contact-opening movements. The discharges investigated here are comparable to discharges generated in the spark test apparatus according to IEC 60079-11 (2011). In this article, the voltage-current characteristics as a function of the discharge length for constant currents of 35 mA-100 mA and maximum voltages of up to 30 V are presented and discussed. The conditions necessary for these discharges are described and the relationship between electrical power, energy and ignition is discussed. An experimental setup is presented in order to analyse discharges that are 200 mu m in length and have a duration of 2-4 ms. The measurement uncertainty is also considered. Further steps for the characterization of electrical discharges and for transfers to other situations are also mentioned. Additionally, spectroscopic investigations of these discharges are discussed in a second article.