The design of an electrical conductivity measurement channel for a shock tube is described. This measurement channel is used for the study of weakly ionized, high-enthalpy flows of gases seeded with alkali salts. The theory for determining the dimensions of the measurement channel and the electrical power supply for the channel is based on Ohm's law. Data are shown which demonstrate that the channel performs well. However, the measured electrical conductivity was one or two orders less than theoretical values. The current traces for each case show that the peak current occurred behind the contact surface, which indicates that some of the seed was entrained behind the test gas originally in the driven tube. An analysis of the effect of Joule heating on the measured conductivity was conducted. The result of increased temperature due to Joule heating in the measurement channel is believed to be minimal. Reasons for the discrepancy are given.