Segmented electrodes are being used extensively in magnetohydrodynamic flow experiments in order to overcome the high impedance present in a continuous electrode system when the plasma has a high Hall coefficient. Until recently the theoretical study of a segmented system has artificially constrained the current to flow directly across the duct. Since this present work was undertaken Witalis has investigated the onset of shorting of the Hall voltage between adjacent segments by leakage currents due to insufficiently long insulator sections, by assuming that the segmentation length is much smaller than the duct width. In this paper three methods are adopted for analysing the effect of leakage currents and obtaining the electrical characteristics. These are conformal mapping, Fourier series and an approximate equivalent circuit. Only the Fourier analysis method requires no further assumptions other than periodicity and it reproduces Witalis's criterion for shorting when his additional assumptions apply. The equivalent circuit method is easier to apply and will be more useful for a practical non-uniform duct.