390 ELEMENTS OF ELECTRICAL ENGINEERING. 



effect depends upon the demagnetizing action of the armature current and it may be 

 best explained by a simple numerical example as follows : Given a generator, with 

 considerable positive brush lead, which is delivering a current of 10 amperes with a 

 total induced electromotive force of 2,500 volts. Under these initial conditions sup- 

 pose that the actual armature flux is 2,500,000 lines, that the leakage flux is also 

 2,500,000 lines, so that the field flux is 5,000,000 lines (coefficient of magnetic leak- 

 age = 2). Let the resistance of the receiving circuit be decreased so that the current 

 output of the generator is increased from 10 to II amperes, or by 10 per cent. This 

 produces a 10 per cent, increase of ampere-turns on the field and a 10 per cent, in- 

 crease of the demagnetizing ampere-turns on the armature, the brushes being fixed in 

 position. The field iron being highly saturated, the 10 per cent, increase of field 

 ampere-turns produces, say, I per cent, increase of field flux making the field flux 

 equal to 5,050,000 lines. Now, the armature core being far below saturation, a very 

 large part of the opposition to the passage of magnetic flux through the armature is 

 due to the demagnetizing ampere-turns of the armature, and a small part only is due 

 to the reluctance of the air gaps and the armature core. Let us suppose, for simpli- 

 city, that all of the opposition to the passage of the flux through the armature is due 

 to the demagnetizing action of the armature current, or in other words, let us suppose 

 that the magnetic reluctance of air gaps and armature core is zero. Then a lo-per 

 cent, increase of armature current would increase the demagnetizing ampere-turns 10 

 per cent., the magnetomotive force (ampere-turns), between the pole pieces will be 

 increased 10 per cent, and the leakage flux will be increased 10 per cent, since the 

 magnetic reluctance of the leakage paths is constant. Therefore the field flux be- 

 comes 1. 01 X 5,ooo,ooo = 5,050,000; and the leakage flux becomes i.ioX 

 2,500,000 = 2,750,000 ; so that the armature flux becomes (5,050,000 2,750,000) 

 which is equal to 2,300,000. The total induced electromotive force is therefore re- 

 duced in the ratio of 2,500,000 to 2,300,000 or in the ratio of i.oo to 0.92. This 

 shows that under the assumed conditions an actual decrease of 8 per cent, in the total 

 induced electromotive force has resulted from a lo-per cent, increase of current. 



Problem : The combined reluctance of the armature core and the air gaps is in 

 fact nearly constant, since the armature core is not highly saturated. Assuming that 

 half of the opposition to the passage of flux through the armature and air gaps is due 

 to this reluctance, and half is due to the demagnetizing ampere-turns on the armature, 

 calculate : (a} The percentage decrease in total induced electromotive force under the 

 above conditions when the current is increased 10 per cent., and (b] The coefficient 

 of magnetic leakage with increased current. Answer : (a] 5 per cent.; (b] 2.15. 



27. The ampere-ohm characteristic of the series generator. For 



some purposes it is convenient to represent the current output of 

 a series generator as a function of the resistance of the receiving 

 circuit, by plotting the values of current output as ordinates, and 

 the corresponding values of resistance of the receiving circuit as 

 abscissas. Fig. 23 shows such an ampere-ohm characteristic of 



