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SCIENCE AND PRACTICE. 287 



resistances, we are now in a position to find the value of the 

 current in any part of the circuit. 

 Substituting in (4. the value of 

 . E-IE 



' 1= ~^~~ ; 

 and of 



. E IE 



we have 



E-EI E-EI 



, 2 



"Whence the current in the lower circuit, between a and b, is 



I = E _ r i + r s (5 



' 



K 



which, inserted in the equations (2. and (3., gives us the 

 currents in the branch circuits : 



and 



If, further, we desire to find the resistance E,' of the whole 



circuit, we must insert the value of I, (5. in the fundamental 

 p 



formula, I = , from which 



E' = E + r \ r * - .... (8. 

 r +r 2 



Of this, E, is the resistance of the undivided circuit between 



a and b, and the fraction - 1 expresses the resistance of 



r l +r 2 



the shunt circuit between the same points ; therefore, the 

 resistance of two parallel conductors is equal to the product 

 divided by the sum of their resistances. 



This must be true for every value of r 2 between and oo ; 



