358 ELEMENTS OF ELECTRICAL ENGINEERING. 



If the torque which acts upon the wheel is greater than the drag 

 of friction, the wheel gains angular velocity, and if the torque 

 which acts upon the wheel is less than the drag due to friction, 

 the angular velocity of the wheel decreases. 



To maintain a constant current in a circuit, an electromotive 

 force equal to Ri must act upon the circuit to overcome the 

 resistance of the circuit. If the electromotive force which acts 

 upon the circuit is greater than Ri, the current increases in value, 

 and if the electromotive force which acts upon the circuit is less 

 than Ri, the current decreases in value. Let the electromotive 

 force which acts upon a circuit exceed Ri by the amount e, 

 then we have : 



-4 A 



in which L is the inductance of the circuit, and dijdt is the 

 rate at which current increases. When e is negative (electro- 

 motive force less than Rt) then di\dt is negative, that is, the 

 current decreases. 



Mechanical analog of equation (2). Whenever an unbalanced 

 force e acts upon a body of which the mass is Z, the body 

 gains velocity at a rate dijdt such that 



C = L (force equals mass times acceleration) 



at 



Starting from the fact that force equals mass times accelera- 

 tion, it can be shown that the kinetic energy of a moving 

 body is equal to one half its mass times its velocity squared. 

 The same argument reversed would show that force must be 

 equal to mass times acceleration if kinetic energy is equal to one 

 half mass times velocity squared ; and an exactly similar argu- 

 ment would establish equation (2) on the basis of equation (i). 



4. Self-induced electromotive force. Reaction of a changing 

 current. When one pushes on a wheel, causing its speed to in- 

 crease, the wheel reacts and pushes back on the hand. This re- 

 acting torque is equal and opposite to the acting torque which is 



