ADVANCED ELECTRICITY AND MAGNETISM. 



where R is the proportionality 

 factor inequation (i), L is the 

 mass of the boat, E is the 

 constant propelling force, and 

 i is the velocity of the boat t 

 seconds after E begins to act. 



_ 

 R R 



(4) 



where R is the resistance of 

 the circuit, L is the inductance 

 of the circuit, E is the con- 

 stant propelling electromotive 

 force, and i is the current in 

 the circuit / seconds after E 



begins to act. 



Equation (4) is plotted as a curve in Fig. 430, in which abscissas 

 represent elapsed times / and ordinates represent the increasing 

 values of the current i. 



37. The stopping of a boat. 



A boat is moving at given 

 velocity I, and the propelling 

 force suddenly ceases to act. 

 It is required to find an alge- 

 braic expression for the de- 

 creasing velocity i of the boat, 

 on the assumption that the 

 frictional drag of the water is 

 exactly proportional to i, or 

 equal to Ri. 



The frictional drag of the 

 water is a force Ri which op- 

 poses i. Therefore the force 

 Ri is to be considered as nega- 

 tive, and, according to Art. 33, 

 we have: 



- - 



1 1 is evident from this equation 



Decay of current in a circuit. 

 A current / is flowing in a 

 circuit, and the propelling elec- 

 tromotive force suddenly ceases 

 to act. It is required to find 

 an algebraic expression for the 

 decreasing current i in the 

 circuit. 



The flow of current is op- 

 posed by a kind of frictional 

 drag (an electromotive force) 

 which is equal to Ri. There- 

 fore the electromotive force Ri 

 is to be considered as negative, 

 and, according to Art. 33, we 

 have: 



- ** = L j t <*> 



It is evident from this equation 



