I$0 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



the current decreases at such a rate that the self-induced elec- 

 tromotive force (reaction of the changing current) L difdt is 

 equal to Ri. This condition is expressed by the equation 





(53) 



and this equation may be most easily interpreted as follows : The 

 electromotive force which is acting on the circuit is equal to zero 

 and this electromotive force is divided into the two parts, Ri 

 which is used to overcome the resistance and L di\dt * which is 

 used to cause the current to change. 



Examples. (a) The canal boat mentioned in example (a) of 

 the preceding article is brought up to a speed of 4 feet per second 

 and then the propelling force ceases to act. The drag of the 

 water is of course equal to 4/5 of 50 pounds when the velocity 

 is 4 feet per second, and this dragging force of 40 pounds pro- 

 duces a negative acceleration or retardation of 0.0064 ft per 

 second per second. The rate at which the kinetic energy of the 

 boat is being dissipated in overcoming the frictional drag of the 

 water may be found by multiplying the frictional drag of 40 

 pounds by the velocity of 4 feet per second which gives 160 

 foot-pounds per second. 



() A current of 4 amperes is established in the circuit which 

 is specified in example ($) of the preceding article. At a given 

 instant the circuit is closed on itself and the current is left to die 

 away. At this instant the value of Ri is 40 volts, that is, the 

 electromotive force required to overcome the resistance of the 

 circuit when the current is 4 amperes is 40 volts and this elec- 

 tromotive force comes from the reaction of the decreasing current, 

 so that the current must be decreasing at a rate of 20 amperes per 

 second according to equation (49). The rate at which the kinetic 

 energy of the current is being dissipated in overcoming the resist- 

 ance of the circuit may be found by multiplying the value of Ri 



* This part must of course be negative, and therefore di\dt is negative, that is, the 

 current i is decreasing. 



