314 



ELEMENTARY LESSONS ON [CHAP. vi. 



student will also now have no difficulty in perceiving 

 why a " long coil " galvanometer, or a " long coil " 

 electromagnet, or instrument of any kind in which the 

 conductor is a long thin wire of high resistance, must not 

 be employed on circuits where both R and r are already 

 small. He will also understand why, on circuits of great 

 length, or where there is of necessity a high resistance 

 and a battery of great electromotive force is employed, 

 " short-coil " instruments are of little service, for though 

 they add little to the resistances their few turns of wire 

 are not enough with the small currents that circulate in 

 high -resistance circuits; and why "long -coil" instru- 

 ments are here appropriate as multiplying the effects of 

 the currents by their many turns, their resistance, though 

 perhaps large, not being a serious addition to the exist- 

 ing resistances of the circuit. 



353. Divided Circuits. If a circuit divides, as in 

 Fig. 129, into two branches at A, uniting together again 



at B, the current will also 

 be divided, part flowing 

 through one branch part 

 through the other. The 

 relative strengths of cur- 

 rent in the two branches 

 will be proportional to 

 their conductivities, z>., 

 inversely proportional to 

 be a wire of 2 ohms re- 



Fig. 129. 

 their resistances. Thus, if r 



sistance and r' 3 ohms, then current in r: current in 



4=3':2, 



or, -| of the whole current will flow through r, and -f- of 

 the whole current through /. 



The joint resistance of the divided circuit between A 

 and B will be less than the resistance of either branch 

 singly, because the current has now choice of either path. 

 In fact, the joint conductivity will be the sum of the two 



