474 Conditions of Self- Excitation in a Dynamo Machine. 



external electric resistance x, there will be a limit in speed 

 below which the machine will refuse to excite itself, the least- 

 speed of self- excitation (called by some authorities the " dead 

 turns," by others the "critical velocity ") being given by the 

 equation 



-=ttf ( 10 >- 



This throws some light on the observed fact that very small 

 machines are not self-exciting except at very high speeds. 

 The fixed part a of the magnetic resistance varies in similar 

 machines of different size, inversely as the linear dimensions ; 

 also the fixed part a of the electric resistance varies inversely 

 as the linear dimensions of the machine. Hence the least- 

 speed of self-excitation in similar machines (on short-circuit^ 

 varies inversely as the square of the linear dimensions. In 

 practice it is possible, in larger sizes of machine, to reduce 

 both a and a to amounts relatively smaller ; for the actual 

 air-space left for clearance may be relatively smaller in large 

 machines, and a relatively greater thickness of copper on the 

 armature -periphery is admissible. When the machine is on 

 short-circuit, x = 0, and the last equation then becomes 



Wl= SKJS C 11 ) 



This, too, is important as showing that the least-speed of self- 

 excitation of a machine while short-circuited is a measure of 

 the goodness of the magnetic circuit. 



For a shunt-wound dynamo the fundamental equation 

 becomes 



(* + f)(a + *+^)=4irnCZ; . . . (12) 



where a is, as before, the resistance of the armature-circuit 

 within the machine, s the resistance of the exciting shunt- 

 circuit, and Z the number of convolutions of the shunt-coil. 

 Excitation does not take place at a given speed n unless x 

 has as its minimum value 



. . . (13) 



47T92CZ — ct [a + s)' 



On open circuit, when # = oo , the least-speed of self-excitation 

 is 



ct(a + s) , 



* 1== 47rC^ < 14 ) 



the machine then exciting itself through its own circuit as a 



