94 ELECTRICAL ENGINEERING 



the integral of this is 



. _ _ R + RI r 



L 



where log C is the constant of integration. This reduces to 



_R_Rj 



r<* L 



when t 0, i = I, and C = L 



Substituting this value, the current is 



-/ L ; (133) 



or 



i=|e Z (133o ) 



The e.m.f. generated in the coil, at the time t, is 



R + RI R + R *t 



When t = 0, the generated e.m.f. is 



* = B T'; ( 134fl ) 



therefore the e.m.f. generated in the circuit is greater than the 



impressed e.m.f. in the ratio 



K 



If, when the impressed e.m.f. is removed, the circuit is short- 

 circuited, RI = and the generated e.m.f. is 



that is, the e.m.f. does not rise. 



But if the circuit is broken RI = oc and e& = oc , and danger- 

 ous e.m.f .'s are generated in the circuit. A large value of RI 

 causes the current to decrease rapidly, but it also causes a high 

 e.m.f. to be generated. 



The energy supplied to the circuit while the current is start- 

 ing is 



= r 



but 



