Certain conditions can require a three-phase induction motor to be operated on a single-phase supply. The proper sizing of the required auxiliary capacitor to meet certain criteria has been discussed, both for constant and for electronics-based variable capacitors. Generally, constant motor parameters are assumed. However, as of a certain motor size, and hence, slot depth, the rotor impedance varies with slip because of skin effect. In this paper, we discuss the influence of this phenomenon on the motor performance, focusing on the peculiarities of single-phase operation. The analysis not only includes Y- and Delta-connected motors but also a third type of connection that we refer to as "Y-segregated leg-connection" and that has not yet found much attention.