PROBLEMS. 505 



the counter electromotive force of one motor in Fig. 49, Appendix B, is 500 volts 

 minus 0.5 X z an d the counter electromotive force of the two motors when they are 

 connected in series is 500 minus 2 X -5 X *' Hence for given current i in each motor 

 the counter electromotive force per motor is 500 volts 0.5 X * when the motors are 

 in parallel and ^ (500 volts 2 X -5 X when the motors are in series ; and the 

 speeds corresponding to the given current i are to each other as these counter electro- 

 motive forces. 



213. The curve in Fig. 50, Appendix B, gives the relation be- 

 tween the tractive effort developed by a single motor and the 

 current in the motor. Derive the curve showing the relation 

 between the total tractive effort and the total current taken from 

 the trolley wire for two motors : (a) connected in parallel, and (b) 

 connected in series. Ans. Coordinates of one point : (a) tractive 

 effort 2,250 pounds, current 160 amperes; (b) tractive effort 

 2,250 pounds, current 80 amperes. 



Note. To make these transformations it is only necessary to remember that a cer- 

 tain current in a motor means so much tractive effort. 



214. The curves derived in problems 212 and 213 for two 

 motors connected in series apply to the two motors on a fifteen- 

 ton car, with 500 volts between trolley and rail, and with no re- 

 sistance in series with the motors. Under these conditions the 

 car travels at a speed of 6.85 miles per hour up a 6.25 per cent, 

 grade. Find (a) The current taken from the trolley ; (b) the 

 total tractive effort developed ; (<r) the total power delivered to 

 the car ; (d) the net power represented by the total tractive ef- 

 fort at the given speed ; and (e) the efficiency of the car equip- 

 ment under the specified conditions. Ans. (a) 80 amperes ; (b) 

 2,250 pounds; (c) 40 kilowatts; (d) 30.65 kilowatts; (e) 76.6 

 per cent. 



Note. See explanation of example in Art. 38 of Appendix B. 



215. The magnet core of a 4-pole shunt dynamo has a diame- 

 ter of 8 inches, including thickness of brass bobbin plus inside 

 insulation. The bobbin is wound with wire to a depth of i y z 

 inches. The terminal voltage of the machine is 1 10 volts, of 

 which 20 per cent, is to be absorbed in the field rheostat. Two 

 thousand ampere-turns are to be provided by each of the four 



