ELECTRIC MOMENTUM. INDUCTANCE. 147 



cause the velocity of the boat to increase. As the boat gains 

 more and more velocity, however, a larger and larger portion 

 of the force E is used to overcome the frictional drag of the 

 water, and a smaller and smaller portion of E is used to 

 cause the velocity of the boat to increase. Finally, after the 

 force has been acting for some time, the boat reaches full speed, 

 and then all of the force E is used to overcome the frictional 

 drag. - 



An electromotive force E due to a battery or dynamo begins 

 to act on a circuit at a given instant. At this instant the current 

 is zero, and the whole of E acts to cause the current to increase 

 in accordance with equation (49). As the increasing current 

 reaches larger and larger values, however, a larger and larger 

 portion of E is used to overcome the resistance of the circuit, 

 and a smaller and smaller portion of E is used to cause the 

 current to increase. After the electromotive force has been act- 

 ing for some time the current reaches its full steady value, and 

 then the whole of E is used to overcome resistance. The por- 

 tion of E which is used at any given instant to overcome resist- 

 ance is equal to Ri and the portion which is used to cause the 

 current to increase is equal to L'difdt. Therefore we have 



E=Ri+L d j t (31) 



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

 and dildt is its rate of increase at that instant. 



Examples. (a) A force of 50 pounds propels a canal boat at 

 a speed of 5 feet per second. Let us assume that the drag of the 

 water is proportional to the velocity of the boat, and let us con- 

 sider what takes place during the time that the boat is being 

 started from rest by a steady force of 50 pounds, the mass of the 

 boat being 100 tons. At the very start, whjen the velocity of 

 the boat is zero, the drag of the water is zero, and the propelling 

 force of 50 pounds is used solely to produce acceleration; there- 

 fore, from the formula F = ^ ma, we find the acceleration a 



