INDUCED ELECTROMOTIVE FORCE. 135 



power electrically may be accomplished by transmitting the large 

 current output of a low voltage generator, or by transmitting the 

 small current output of a high voltage generator. In the former 

 case very large and expensive transmission wires must be used or 

 the loss of power in the transmission wires will be excessive. In 

 the latter case, comparatively small and inexpensive transmission 

 wires may be used without involving an excessive loss of power. 

 Therefore high electromotive force is a practical necessity in the 

 long distance transmission of power. The user of electric power 

 must however be supplied with current at low electromotive 

 force, partly on account of the danger involved in the use of high 

 electromotive forces, and partly on account of the fact that many 

 types of electrical apparatus cannot be operated satisfactorily with 

 high electromotive force ; also it is inconvenient and dangerous to 

 generate very high electromotive forces in a complicated machine 

 like an alternator which must be cared for by an attendant. 

 These difficulties are met by employing a transformer for step-up 

 transformation at the generating station and another transformer 

 for step-down transformation at the receiving station. 



High efficiency of the transformer. The transformer is not only 

 cheap to construct and cheap to operate, but it is extremely 

 efficient. The efficiency ranges from 95 or 96 per cent, for 

 small sized transformers to 98 per cent, or more for transformers 

 of large size. 



73. Current and electromotive force relations of the transformer. In the 



foljowing discussion Z 1 represents the number of turns of wire in the primary coil, 

 and Z" the number of turns of wire in the secondary coil. The effect of the elec- 

 trical resistance of the coils, which is usually quite small in practice, is ignored, and 

 all of the magnetic flux which passes through one coil is assumed to pass through the 

 other coil also. 



(a) Electromotive force relations. Let E f be the effective value of the alter- 

 nating electromotive force which acts on the primary coil of a transformer, and let E tf 

 be the effective value of the electromotive force induced in the secondary coil of the 

 transformer. Then 



/ Z ' 

 E" ~~Z 



This relation may be shown to be true as follows : The only thing which opposes the 

 flow of current through the primary coil is the reacting electromotive force induced in 



