SINGLE-PHASE COMMUTATOR MOTORS 391 Volt-ampere Input: Power-factor: Efficiency: Apparent Efficiency: r, = P n = p--, (44) (45) (46) (47) etc. 216. While excessive values of the short-circuit current under the commutator brushes, f*, give bad commutation, due to ex- cessive current densities under the brushes, the best commuta- tion corresponds not to the minimum value of /4 — as the zero value at synchronism in the repulsion motor — but to that value of /4 for which the sudden change of current in the armature coil is a minimum, at the moment where the coil leaves the com- mutator brush. J4 is the short-current in the armature coil during commuta- tion, reduced to the armature circuit, /i, by the ratio of effective turns: short-circuited turns under brushes total effective armature turns , ^ The actual current in the short-circuited coils during commuta- tion then, is: It = -, (49) or, if we denote: X4 (50) where A* is a fairly large quantity, and substitute (24), it is: ZK (51) Before an armature coil passes under the commutator brushes, it carries the current, —/i; while under the brushes, it carries the current, l\] and after leaving the brushes, it carries the cur- rent, 5; < In ,.iğ