TRANSrOKMER. 413 TRANSFORMER. placed at right angles and so that the plane of one coil passes through the centre of the other. If an electric current is passed through one of the coils, magnetic lines of force (see Magnet- ism) will be created, some of which will thread through the second coil. If the coils are placed Iron Core Primary Coil Fig. 1. DIAGRAU OF ESSENTIAL PABTS OF A TEANBFORMER contiguous to each other nearly all of the lines of force created by the first coil will thread through the second coil, and if iron is intro- duced in the magnetic circuit the number of these lines, or the intensity of the magnetic field, will be much greater with a given current in the first coil than if air or other non-magnetic mat- ter only were present. ( See Magnetism. ) A device constituted in this manner of an iron magnetic circuit interlinked with two electric circuits becomes, when one of the electric cir- cuits is supplied with alternating current, an alternating current transformer. Starting with no current in either coil, let us consider what happens if we apply an electro- motive force to the extremities of the first or primary coil. A current will commence to flow, but will not attain at once to the full magni- tude due to the electromotive force applied and the resistance of the circuit. This is because the passage of the current creates a magnetic field, the growth of which in turn creates a counter electromotive force opposed in direction, as the name signifies, to the impressed electromotive force. (See Electricity.) At the same time that the counter electromotive force is produced in the first coil, an induced electromotive force will be created in the second coil, having the same direction as the counter electromotive force in the fir.st coil, or contrary to the electromotive force impressed upon the first coil. Supposing that the second coil is so connected that it forms a closed circuit, an electric current will be set up in it which will be opposite in direction to the current in the first coil. It should be noted that an electromotive force is induced in the second coil only so long as the number of lines of magnetic force is changing. If the first coil is supplied from a source of al- ternating current, this will be continually, since the impressed electromotive force from such a source will increase incessantly from zero to a maximum in one direction, pass back through the zero value to a maximum in the opposite direc- tion, and then fall to zero again. It will be seen that the current in the primary coil will follow a similar cycle of changes, as will also the fiux of lines of magnetic force and the induced elec- tromotive force and current in the secondary coil. It may be assumed that in an ideal trans, former all the lines of force created by the first coil i)as3 through the second coil, and further, that there are no losses of energy due to tlie re- sistance of the two coils, to eddy currents induced in the windings or in the iron core, or to other causes. In accordance with the first assumption that all lines of magnetic force thread through both coils, the electromotive force induced by variations of the magnetic (lux will be llu' same in every turn of either coil, or, in other words, the total electromotive force induced in each coil will be proportional to the number of turns in that coil. If, say, the primarv consists of 100 turns of wire and the secondary coil of 10 turns of wire, and if, furtlier, the jirimarv coil be con- nected with a source of supply of alternating cur- rent having a potential difference of 1000 volts, the potential difference at the extremities of the secondary coil would be 100 volts. Now, while it is seen that the voltages produced are in direct proportion to the number of turns in the respec- tive coils, it will be found that the currents pro- duced bear an inverse ratio. This maj' be ex- plained as follows: Assuming the primary coil to be without re- sistance and also, for the time being, that the secondary circuit is open so that no current can flow, the current in the first coil will be limited entirely by the back electromotive force, and, un- der the conditions assumed of a highly permeable magnetic circuit, this would almost equal the ap- plied electromotive force and little current would flow. However, a current of sufficient magnitude to create the magnetic field producing the counter electromotive force referred to must flow. This magnetizing current and the mag- netic flux it produces will be varying most rapidly when the impressed electromotive force is maximum, since then the counter electromo- tive force must be greatest, and again, it must reach its maxima, that is, its limits, when the impressed electromotive force is zero. In other words, the magnetizing current is not in phase with the impressed electromotive force, but lags behind, and if the matter is considered in detail it will be found that this current takes energy from the circuit during two parts of the cycle and returns it during two others. Energy is absorbed while the magnetic field is being built up and returned to the supply circuit as the field collapses. If at any time much disparity should begin between the impressed electromotive force and the counter electromotive force, the current and magnetic field would commence immediately to vary rapidly, which would tend to bring the two electromotive forces again into approximate balance. Further, the intensity of this mag- netizing current depends only upon the sus- ceptibility of the magnetic circuit, the magni- tude of the electromotive force impressed upon the primary coil, and the frequency with which the impressed electromotive force is reversed. Since the counter electromotive force depends on the rate at which the lines of force are created or die out witliin the coil, if the frequency is great, the magnetic flux, and therefore the magnetizing current, will not need to reach as high values for a given applied electromotive force as if the frequency were low. It has just been pointed out that in the ideal transformer without resistance or other losses the coiniter electromotive force prevents any flow of current in the primary in phase with the im-
