I. General 110. The alternating-current transformer consists of a magnetic circuit interlinked with two electric circuits, the primary, which receives power, and the secondary, which gives out power. Since the same magnetic flux interlinks primary and second- ary turns, the same voltage is induced in every turn of the electric circuits, and the e.m.fs. induced in the primary and in the secondary winding therefore have the ratio of turns: «'i ni —r — — = a. . e'2 n2 This ratio is called the ratio of transformation. The ratio of transformation of a transformer is the ratio of turns of primary and secondary windings. In addition to the induced e.m.fs. e'i and e\, resistance r and reactance x consume voltage in primary and secondary wind- ings. The voltage consumed by the resistance represents waste of power; the voltage consumed by reactance is wattless, but causes lag of current, that is, lowers the power factor; while the in- duced voltages give the power transfer from primary to sec- ondary. Efficiency therefore requires to make the former vol- tages as small as possible, and the induced voltages as near to the terminal voltages as possible. Therefore, in first approxi- mation, the ratio of the terminal voltages e\ and e% is the ratio of transformation: As, approximately, the power output of the secondary equals the power input into the primary, it is: hence, ti 1 277 278 ELEMENTS OF ELECTRICAL ENGINEERING that is, the transformer changes from voltage e\ and current i\ to voltage 62 = — and current iz = aii. In general either of the two transformer circuits may be used as primary or as secondary, and by their use transformers thus are distinguished as step-down transformers, if the primary voltage is higher than the secondary, and step-up transformers, if the secondary voltage is higher. Instead of the expression "primary" and "secondary," constructively it therefore is preferable to speak of "high voltage winding" and "low voltage winding." 111. The foremost use of the transformer therefore is for changing of the voltage: From the medium high primary distribution voltage (2300) to the low secondary consumer voltage (110, 220). From the high transmission (30 to 150 kilovolts) to the primary distribution voltage (2300) or the voltage required by syn- chronous motor, synchronous converter, etc. From the low or medium high generator voltage to the high transmission voltage. Other occasional uses of transformers are: To electrically tie systems together, so as to permit exchange of power between them, and synchronous operation. In this case, depending on the distribution of the load in the system, either transformer winding may be primary or secondary. To break up electrically a very large system, so that a ground in one part does not ground the entire system. In this case, the transformer ratio usually is 1 -f- 1. In all these cases, the transformers are "constant potential transformers," that is, primary and thus secondary voltage are constant or approximately so. Transformers supplied with constant current in the primary give practically constant current in the secondary, at a primary voltage varying with the secondary voltage. Such transformers are used in constant-current circuits, for supplying meters in high voltage circuits, etc. Further uses of transformers are for operating instruments, switches, etc., in high voltage systems. In this case, the trans- formers may be potential transformers — connected across the constant voltage circuit, or current transformers — connected in series into the circuit, for the supply of meters, the opera- tion of overload circuit breakers, etc. ALTERNATING-CURRENT TRANSFORMER 279 • Where not expressly stated otherwise, in general a constant potential transformer is understood.