ELECTRIC CIRCUITS 95 



therefore, 



of this I Ri 2 dt is the energy transformed into heat in the electric 

 Jo 



r 1 



circuit, and I Li di is the energy stored in the magnetic field. 



Jo 



The energy in the magnetic field is 



/>/ 72 



W M = I Lidi = L-^ 

 Jo * 



and is independent of the resistance of the circuit. 



This magnetic energy is returned to the electric circuit while 

 the current is stopping and prevents it from immediately falling 

 to zero. It is transformed into heat in the circuit and is 



W = f i* (R + R,) dt, 



Jo 



but 



i = Ie~ 

 therefore, 



r 2 ut-t- 

 e L 



the integral of this is 



_ 2 (* + *.), 



and 



-1 (H ~r KI) n/r> i D\l e In' 



J2 



W = L--as before. 



If the circuit is broken this amount of energy must be dis- 

 charged and produces a spark. 



69. Example. The shunt field winding of a 6-pole, 125-volt, 

 direct-current generator has 500 turns per pole and carries 12.5 

 amperes; the resistance of the field winding is 7.5 ohms and the 



125 



resistance of the field rheostat is -^-= 7.5 = 2.5 ohms; and the 



LZ.o 



flux per pole is 6.3 X 10 6 lines; determine: 



