PROBLEMS. 473 



approximately equal to the reciprocal of the current density in amperes per square 

 inch of contact surface. An elaborate discussion of brush contact resistance in its de- 

 pendence upon peripheral velocity of commutator, brush pressure, quality of carbon, 

 and current density is to be found in E. Arnold's Die Gleichstrommaschine, Vol. I., 

 pp. 478-484. 



112. The generator specified in problem 106 has its field sepa- 

 rately excited so as to give its full rated voltage at zero-load. 

 Assuming that this constant field excitation leads to the produc- 

 tion of a constant total induced electromotive force, E a , at all loads, 

 find : (a) the value of the resistance of the external circuit for 

 which the power output of this separately excited generator is 

 the greatest possible ; (b) the corresponding value of the current ; 

 (<r) the value of this maximum power output ; (d) the correspond- 

 ing terminal voltage of the generator ; and (e) the corresponding 

 electrical efficiency of the generator. Ans. (a) 0.29 ohm; (b) 

 198.3 amperes ; (c) 1 1,400 watts ; (d) 57.5 volts ; (e) 50 per cent. 



NOTE. The armature current corresponding to maximum possible output of a 

 generator (or motor) is greatly in excess of the greatest permissible armature current 

 and it would cause excessive sparking at the brushes and excessive overheating of the 

 armature windings. The assumption of constant armature flux 4> is made to simplify 

 the problem. In fact the armature flux falls off greatly with such excessive armature 

 currents. 



113. Assuming that the armature flux, <I>, of the motor speci- 

 fied in problem 78 is constant at all loads, find : (a) the value of 

 the counter electromotive force and speed of the motor for which 

 its power output has the greatest possible value , (ft) the value of 

 this greatest possible output; and (c) the efficiency of con version 

 of the motor at its greatest possible power output, ignoring the 

 power delivered to its field winding. Ans. (a) 55 volts and 500 

 revolutions per minute; (b) 27,171 watts ; (e) 50 per cent. 



NOTE. See note to problem 112. 



114. A certain belted compound-wound machine, purchased 

 second-hand, is rated as a 25O-kilowatt 5 50- volt generator, at a 

 speed of 320 revolutions per minute. The diameter of the arma- 

 ture is 46 inches and the gross length of the armature core is 

 12.3 inches. Calculate the rating of this machine according to. 



