INDUCTANCE AND CAPACITY. 359 



causing the increase of speed. When the speed of a wheel is 

 increasing, the reaction of the wheel is a torque in a direction 

 opposite to the motion, when the speed of a wheel is decreasing 

 the reaction is a torque in the direction of the motion. Similarly 

 when an electromotive force acts upon a circuit and causes a cur- 

 rent to increase or decrease, the changing current reacts ; the 

 reacting electromomotive force is equal and opposite to the acting 

 electromotive force, L x dijdt, which is causing the current to 

 change ; when the current is increasing, the reaction of the cur- 

 rent is an electromotive force opposed to the current ; and when 

 the current is decreasing, the reaction is an electromotive force in 

 the direction of the current. The reaction of a changing current 

 is called self -induced electromotive force. 



5, Differential equations of growing and decaying currents. 



A constant electromotive force S is at a given instant connected 

 to a circuit of which the resistance is R and the inductance is 

 L ; after the current becomes fully established it is equal to /R 

 according to Ohm's law, but during the time that the current is 

 being established a portion of & is used to overcome the resist- 

 ance of the circuit and a portion of 8 is causing the current to 

 increase. The portion used to overcome resistance is equal to 

 Ri, and the portion used to cause the current to increase is equal 

 to Ldijdt, and therefore we have 



= * + (3) 



in which i is the value of the growing current at a given instant, 

 and dijdt is its rate of increase. 



When a circuit in which a given current is flowing, is short- 

 circuited and left to itself without any electromotive force acting 

 to maintain the current, the current dies away ; in this case equa- 

 tion (3) becomes 



o = Ri + L~ (4) 



