INDUCED ELECTROMOTIVE FORCE. 131 



and flows through two distinct paths in the armature winding to 

 reach the positive brush. In the particular multipolar dynamo 

 shown in Figs. 90 and 91 the current enters the armature through 

 three brushes, and the current which enters at each of the three 

 brushes divides into two parts and flows through two distinct paths 

 to reach a positive brush. Therefore in this particular machine, 

 having six field poles, there are six 'current paths through the 

 armature from negative to positive brushes.* 



70. Fundamental equation of the direct-current dynamo. Let 4> be the mag- 

 netic flux which enters the armature from the north pole of the field magnet and leaves 

 the armature at the south pole of the field magnet, let Z be the number of conductors 

 on the outside surface of the armature, let n be the speed of the armature in revolu- 

 tions per second, and let E a be the electromotive force induced in the armature wind- 

 ing. A voltmeter connected to the brushes of the dynamo would indicate the value 

 of E a if the current in the armature were negligibly small ; when the current in the 

 armature is large, a portion of E a is used to overcome the armature resistance. The 

 equation which expresses the relation between E a , *, Z, and n is called the funda- 

 mental equation of the dynamo. This equation is here derived for the simplest case, 

 namely, that of a bipolar dynamo with simple ring-wound armature. In this case 



E a = <bZn abvolts (45 a ) 



or 



Proof of equation (450). During i/n second the armature makes one complete 

 revolution, so that during i/2n second a given conductor sweeps past a field pole 

 from a to b in Fig. 86 and cuts $ lines of force. Therefore this conductor cuts 

 lines of force at an average rate which is equal to 4>-f- i/2, or 2<t> lines of force 

 per second ; which is equal to the average electromotive force induced in the given 

 conductor during the time that it is moving from a to b in Fig. 86 ; also this is the 

 average electromotive force in all of the conductors between a and b at any instant. 

 Therefore, since there are Z/2 armature conductors or wires in series between a 

 and b, the electromotive force between a and b is equal to Z/2 X 2 *> or 

 Eg. = $Zn abvolts. 



71. The induction coil.f An iron rod wound with insulated 

 wire may be repeatedly magnetized and demagnetized by con- 

 necting a battery to the winding and repeatedly making and 

 breaking the circuit. The increasing and decreasing magnetic 



* A type of armature winding which is frequently employed provides but two paths 

 through the armature winding irrespective of the number of field magnet poles. 



f The induction coil was invented by Kuhiukorft in 1855 and it is frequently called 

 the Ruhmkorff coil. 



