ELEMENTARY THEORY OF ELECTROMAGNETISM. 45 



30. Electromotive force relations of the alternating-current 

 transformer. Figure 36 is a diagram showing one coil of a 

 transformer connected to i,ioo-volt alternating-current street 

 mains, and the other coil of the transformer delivering current to 

 house wires. A remarkable thing about a transformer is that 

 the primary coil may have, say, one ohm of resistance and yet 

 but very little current will flow through it when it is connected 

 directly across i,ioo-volt mains. As a matter of fact the electro- 

 motive force (the back electromotive force b as described below) 

 which is induced in the primary coil by the magnetic reversals 

 of the transformer core is at each instant opposite to and very 

 nearly equal to the electromotive force across the supply mains. 



alternating-current 

 supply mains 



1100 volts 



&QMMMJZ' turns 

 Z n turns 



house wires 

 110 volts 



Fig. 36. 



It is very difficult to make an intelligible argument concerning 

 an alternating electromotive force or current unless some simple 

 scheme is used to represent successive instantaneous values of elec- 

 tromotive force or current. Imagine the line E' ', Fig. 37, to rotate 

 uniformly about in the direction of the arrow /, the number 

 of revolutions per second of the line being equal to the number 

 of cycles per second of the alternating electromotive force across 

 the supply mains in Fig. 36. Then the length of E r may be 

 chosen so that its projection e' on the fixed line cd represents 

 the actual electromotive force between the supply mains in Fig. 

 36 at each instant. 



