A condenser, on account of its capacity, causes an a.-c. current to lead the voltage, that is the current reaches its maximum value before the voltage does. In this respect a condenser has an effect opposite to that of the self-induction of a choke coil (the latter causing the current to "lag"). (See Fig. 435.)
437. Transmission of Electric Power.—A field of peculiar usefulness for a.-c. currents is in the economical transmission of electric power. This fact is due to the following reasons: (a) The loss of electrical power in a transmission line is due to the production of heat; the heat produced being proportional to I2R, or to the square of the current intensity. Any lessening of the current flow required to transmit a given power will therefore increase the efficiency of transmission. (b) In order to employ a small current in transmitting a large amount of power, we must use a very high e.m.f. Such high electromotive forces, say from 60,000 to 100,000 volts, can be obtained only by the use of a.-c. transformers, since it is not practicable to build a direct current generator capable of producing 60,000 volts. In large power transmission systems, a.-c. generators are used to produce powerful alternating currents. The e.m.f. is then stepped up to a suitable voltage (2300-100,000) by transformers and sent over transmission lines to the various places where the power is to be used; at these places suitable transformers "step-down" the e.m.f. to a convenient or safe voltage for use. (See Fig. 442 of a transmission line and Fig. 438 of a large power transmission system, and Fig. 439 of an a.-c. generator and power plant.)
Fig. 438.—Diagram of an alternating current high tension power system. (A) Alternator, (Tu) water turbine, direct connected to alternator, (E) exciter, (T1) step-up transformers in power station, (T2) step-down transformers in substation, (M) motor, (L) lamps, single-phase, three-wire system, (T3) step-down transformers delivering three-phase current to rotary converter (R) which delivers direct current to the trolley line.
438. Power Factor.—The power factor is a matter of interest and importance in the use of a.-c. machines. Its meaning and use may be learned from the following explanation: In a direct current circuit, watts equals volts times amperes. In an alternating current circuit, this equation is true only when the current is "in step" with the voltage, that is, only when there is no inductance or capacity in the circuit. If current and voltage are out of step, i.e., if there is lag or lead (see Fig. 434), the product of volts and amperes gives only the apparent power, the ratio between true and apparent power depending on the amount of lag or lead. This ratio is called the power factor. In an a.-c. circuit, then, the power equation is: watts = volts × amperes × power factor, or power factor = true power/apparent power. The product of volts and amperes is the apparent power and is called volt-amperes in distinction from the true power or watts. Therefore the following is true: power factor = true watts/volt-amperes.
Fig. 439.—Power house showing alternators, direct connected to horizontal hydraulic turbines. Note the direct current "exciter" on end of shaft of alternator. (Courtesy of General Electric Co.)
439. Single-phase Currents.—There are several kinds of a.-c. currents. One of the most common is the single-phase. It is simply the common a.-c. current used for light and power in the average home, and uses a two-wire circuit around which the current is rapidly alternating. Fig. 440 illustrates the changes of e.m.f. in an a.-c. single-phase current. It may be produced by a single coil rotating in a magnetic field. The curve of Fig. 440 represents one cycle, that is, one complete series of changes in the electromotive forces. At the end of the cycle the armature is in the same condition as at the beginning so far as the magnetic field is concerned. It then begins a new cycle. The ordinary commercial alternating current has a frequency of 60, that is 60 cycles per second. One rotation produces as many cycles as there are pairs of poles. For example, if there are 48 poles in the generator field, one rotation produces 24 cycles.