POWER AND POWER-FACTOR. 69 



100 



SCALE OF" VOLTS 

 1fl 20 30 40 50 60 70 80 9Q 100 



B 



FIG. 31. DIAGRAM OF B.M.P. FOR ARC LAMP AND CHOKING COIL. 



Let A B represent the total voltage. 

 A C represent voltage of arc. 

 B C represent voltage of coil. 



Produce A C and from B draw B D perpendicular to 

 AC, cutting it in D. Then the A B DC will be the 

 A of voltages for the coil, D C being the energy voltage 

 in phase with the current, and D B being the self-induction 

 voltage. The power lost in the coil will be the product 

 of the voltage represented by D C x current in the 

 circuit. The voltage represented by D B is the product 

 of the reactance of the coil x current = 2 IT n L x C. 

 Consequently the coil would have to be designed so as to have 

 the self-induction L obtained in this way. This may be 

 put in other words by saying that the back voltage of the 

 coil must be the voltage represented by D B. 



Calculation. As an example to illustrate the preceding 

 statements, the following example of a choking coil and 

 arc lamp are given. The figures are those for which Fig. 

 31 is drawn. 



An arc lamp requires 40 volts and 10 amps., a choking 

 coil being put in series with it to reduce the current to 

 the required value. The voltage of supply is 100 volts. 

 It is found by calculation, the details of which are 

 explained later, that the power spent in heating the 

 windings and overcoming hysteresis and eddy current 

 losses is 168 watts. 



