RESISTANCE AND ELECTROMOTIVE FORCE. 49 



26. Typical problem in branched circuits. The battery in Fig. 

 2. 5 has an electromotive force of 1 5 volts ; the battery and the 

 wires which connect the battery to the points A and B have 

 a total resistance of 2 ohms ; the upper branch has a resistance 

 of 3 ohms (R! = 3) and the lower branch has a resistance of 4 

 ohms (R" = 4) , and it is required to find : (a) the combined 

 resistance of the two branches and total resistance of the circuit, 

 (^) the total current, (^) the electromotive force between the 

 branch points, (d} the current in the upper branch, and (e) the 

 current in the lower branch. 



(a) The combined resistance of the two branches is the recip- 

 rocal of (^ -f ^), or Jy 2 - of an ohm. Therefore the total resistance 

 of the circuit through which the battery sends current is 3|- 

 ohms. 



(&) The total current is found by dividing the electromotive 

 force of the battery by the resistance of the circuit, which gives 

 4A amperes. 



(c] The electromotive force between the branch points is equal 

 to the product of the total current by the combined resistance 

 of the two branches or to 4^ amperes times ify ohms, which 

 gives 6|| volts. 



(d} The current in the upper branch is found by dividing the 

 electromotive force between the branch points by the resistance 

 of the upper branch, which gives 2^ amperes. 



(e) The current in the lower branch is found by dividing the 

 electromotive force between the branch points by the resistance 

 of the lower branch, which gives i^| amperes. 



27. The use of shunts with galvanometers and ammeters. In 

 the use of a galvanometer, or other current-measuring instrument, 

 it is frequently not desirable to send the whole of the current 

 which is to be measured through the instrument. In such a case 

 a definite fractional part of the current may be diverted by mak- 

 ing the instrument one of two branches of the circuit, as shown 

 in Fig. 26a, in which A represents the galvanometer or ammeter 



5 



