The theory of the condenser motor is the operation of a poly-phase motor on a single-phase source. If we consider the current in one phase of a two-phase motor the IR drop is in phase with the current I and the reactance drop is at right angles to it. The voltage OB across the phase is the vector sum of these two.
Now if a condenser is connected in series with this phase the reactance drop across the condenser will be opposite to that in the winding. The voltage across the condenser is BC and the total voltage across the condenser and the phase in series with it is OC. This is the line voltage. If the other phase of a two-phase motor is connected directly across the line the two phases will have voltages impressed on them which are electrically displaced by the angle BOC. By assigning a proper value to the capacitance of the condenser this angle can be made equal to 90 degrees. The voltage OB, however, will not be equal to the line voltage unless the angle BOA is equal to 45 degrees, that is, the power factor of the phase must be 70.7 per cent. It is not necessary to design both phases of the motor for the same voltage so that this condition does not present any great difficulty.