120 ELECTRICAL APPARATUS Erf the numerical value of the imaginary term of $0; the torque ratio is: The volt-ampere ratio is: thus the apparent starting-torque efficiency: (88) (89) (90) etc. 77. Three cases have become of special importance: (a) The resistance-reactance monocyclic starting device; where one of the two impedances, Z\ and Z2; is a resistance, the other an inductance. This is the simplest and cheapest arrangement, gives good starting torque, though a fairly high current consump- tion and therefore low starting-torque efficiency, and is therefore very extensively used for starting single-phase induction motors. After starting, the monocyclic device is cut out and the power consumption due to the resistance, and depreciation of the power- factor due to the inductance, thereby avoided. This device is discussed on page 333 of "Theoretical Elements of Electrical Engineering" and page 253 of "Theory and Calcu- lation of Alternating-current Phenomena." (6) The "condenser in the tertiary circuit," which may be considered as a monocyclic starting device, in which one of the two impedances is a capacity, the other one is infinity. The capacity usually is made so as to approximately balance the mag- netizing current of the motor, is left in circuit after starting, as it does not interfere with the operation, does not consume, power, and compensates for the lagging current of the motor, so that the motor has practically unity power-factor for all loads. This motor gives a moderate starting torque, but with very good start- ing-torque efficiency, and therefore is the most satisfactory single- phase induction motor, where very high starting torque is not needed. It was extensively used some years ago, but went out of use due to the trouble with the condensers of these early days, and it is therefore again coming into use, with the development of the last years, of a satisfactory condenser.