296 Steady Currents in Linear Conductors [CH. ix 



conductor between P and Q. Hence the rate of flow into the section of the 

 conductor across P must be exactly equal to the rate of flow out of this 

 section across Q. Or, the currents at P and Q must be equal. Hence we 

 speak of the current in a conductor, rather than of the current at a point in 

 a conductor. For, as we pass along a conductor, the current cannot change 

 except at points at which the conductor is touched by other conductors. 



Ohms Law. 



340. In a linear conductor in which a current is flowing, we have 

 electricity in motion at every point, and hence must have a continuous 

 variation in potential as we pass along the conductor. This is not in oppo- 

 sition to the result previously obtained in Electrostatics, for in the previous 

 analysis it had to be assumed that the electricity was at rest. In the present 

 instance, the electricity is not at rest, being in fact kept in motion by the 

 difference of potential under discussion. 



The analogy between potential and height of water will perhaps help. A lake in 

 which the water is at rest is analogous to a conductor in which electricity is in equi- 

 librium. The theorem that the potential is constant over a conductor in which electricity 

 is in equilibrium, is analogous to the hydrostatic theorem that the surface of still water 

 must all be at the same level. A conductor through which a current of electricity is 

 flowing finds its analogue in a stream of running water. Here the level is not the same at 

 all points of the river it is the difference of level which causes the water to flow. The 

 water will flow more rapidly in a river in which the gradient is large than in one in 

 which it is small. The electrical analogy to this is expressed by Ohm's Law. 



OHM'S LAW. The difference of potential between any two points of a wire 

 or other linear conductor in which a current is flowing, stands to the current 

 flowing through the conductor in a constant ratio, which is called the resistance 

 between the two points. 



It is here assumed that there is no junction with other conductors 

 between these two points, so that the current through the conductor is a 

 definite quantity. 



341. Thus if C is the current flowing between two points A, B at which 

 the potentials are VA, YB, we have 



V A -V B = CR, 



where R is the resistance between the points A and B. Very delicate ex- 

 periments have failed to detect any variation in the ratio 



(fall of potential)/(current), 



as the current is varied, and this justifies us in speaking of the resistance as 

 a definite quantity associated with the conductor. The resistance depends 

 naturally on the positions of the two points by which the current enters and 

 leaves the conductor, but when once these two points are fixed the resistance 

 is independent of the amount of carrent. 



