302 Steady Currents in Linear Conductors [OH. ix 



Thus we may write 2CR = 2E .............................. (270), 



where the summation in each term is taken round any closed circuit of 

 conductors, and this equation, together with 



2(7 = ................................. (271), 



in which the summation now refers to all the currents entering or leaving a 

 single junction, suffices to determine the current in each conductor of the 

 network. 



Equation (271) expresses what is known as Kirchhoff's First Law, while 

 equation (270) expresses the Second Law. 



Conductors in Series. 



347. When all the conductors form a single closed circuit, the current 

 through each conductor is the same, say C, so that equation (270) becomes 



The sum %R is spoken of as the " resistance of the circuit," so that the 

 current in the circuit is equal to the total electromotive force divided by the 

 total resistance. Conductors arranged in such a way that the whole current 

 passes through each of them in succession are said to be arranged "in series." 



Conductors in Parallel. 



348. It is possible to connect any two points A, B by a number of 

 conductors in such a way that the current divides itself between all these 



FIQ. 96. 



conductors on its journey from A to B, no part of it passing through more 

 than one conductor. Conductors placed in this way are said to be arranged 

 " in parallel." 



Let us suppose that the two points A, B are connected by a number of 

 conductors arranged in parallel. Let R l} R^... be the resistances of the 

 conductors, and C 1} (7 2 ,... the currents flowing through them. Then if V A , V B 

 are the potential at A and B, we have, by Ohm's Law, 



The total current which enters at A is (7 1 + (7 2 + ..., say C. Thus we 

 have 



T7 V 2 



I = = J" = " 



R l JR 2 



