PROBLEMS. 481 



NOTE. The driving torque, not counting that due to the starting coil, is proper 

 tional to the watts delivered to the receiving circuit, and it may be conveniently ex- 

 pressed in "watts." The driving torque due to the starting coil (with given voltage 

 between the supply mains) may be expressed as the difference between the starting 

 watts with and without the starting coil. The running friction (a torque) may be ex- 

 pressed as one half the starting load in watts without the starting coil. The speed of 

 the meter may be conveniently expressed in " watt-hours recorded per hour." 



Subtracting from the total driving torque (including the torque due to the starting 

 coil) the running friction, gives the net torque used to overcome the retarding action 

 of the damping magnets, and the speed of the meter is proportional to this net torque. 

 The torque produced by the starting coil is proportional to the square of the voltage 

 between the mains. 



137. The operation costs of a 40 5 -kilo watt lighting plant 

 including the distributing system are : an invariable charge of 

 $22,000 per year, which includes interest, depreciation, repairs, 

 insurance, taxes, one half of the cost of wages, and one quarter 

 of the cost of fuel and supplies ; and a variable charge of 2.05 

 cents per kilowatt-hour of station output. Find the proper net 

 prices to be charged per kilowatt-hour for : (a) domestic lighting 

 which comes wholly within the daily period of two hours of full 

 station-load ; (&) store lighting of which one third comes during 

 the daily period of full station-load, and (c) motive power no 

 portion of which comes during the period of full station-load. 

 Allow for a profit equal to 1 5 per cent, of the gross income. 

 Ans. (a) 1 1. 1 6 cents, () 5.33 cents, and (c) 2.41 cents. 



NOTE. The separating of the operation costs of a station into an invariable part 

 A and a variable part bP, which is proportional to the station-load P, is only approx- 

 imately correct. The total actual cost of operating the station at various loads may 

 be determined from actual station tests. From these data a curve may be plotted show- 

 ing the costs as ordinates and the station-loads as abscissas. A straight line may now 

 be drawn so as to represent this curve as nearly as may be. Then A is the intercept 

 of this straight line on the j-axis, and b is the tangent of the angle between this straight 

 line and the jr-axis. 



The cost price per kilowatt-hour during the two hours of full load is $22,000 

 divided by 405 X 2 X 3 6 5> to which must be added 2.05 cents ; whereas the cost price 

 per kilowatt-hour during the remainder of the day is 2.05 cents. 



138. Find the proper prices to be charged per kilowatt-hour 

 for the three classes of service specified in problem 137, the daily 

 period of full station-load being three hours. Ans. (a) 8.25 

 cents ; (b) 4.36 cents ; (c) 2.41 cents. 



