Internal Resistance of Batteries. 



467 



Y R = 



V. R 

 B+R 



"Where Y R is the difference of potential of the poles of the 

 battery when they are connected by a resistance of R ohms. 

 Y is the difference of potential of the poles when open. The 

 ratio of Y B to Y was obtained by measuring the charges of 

 the condenser in the two cases, and R was known. 



Our experiments soon showed that it was not worth while 

 to take the trouble to use extremely short times within the 

 limits at our command. The same general facts were seen 

 whether the time were one-half a second or one-thonsandth of 

 a second. In obtaining most of the results given in the follow- 

 ing table the time of closure of the battery poles was about 

 one quarter of a second : in the cases marked with a star, how- 

 ever, the differences of potential were measured by the aid of 

 a quadrant electrometer and the poles were connected for 

 upwards of 60 seconds. 







Resistances of various cells as obtained by measur- 

 ing the difference of potential of the poles when open 

 and when closed by shunts of given resistance. 



Resistances of 

 the same cells as 

 obtained by the 

 use of alternate 

 currents. 





Cells. 



20' 



?he re 

 10- 



sistanc 

 TO 



,es In 

 5-0 



3-36 



ohms 



3-0 



3f the 

 2-0 



3-27 



shunt 

 l'O 



i used 

 0-5 



04 



1 Daniell* 





3-59 



3-31 



326 







2-9 



2 Daniell* 



2-98 



2-90 





2-87 



2-83 



2-78 



2-74 







2-5 



3 Daniell 



30 



3-0 



2-7 





2-4 











2-1 



4 Daniell . 





41 



3-8 



3-7 



35 



3-5 









2-8 



5 Gravity 





3-4 



3-3 



3-2 





3-0 



2-7 







2*2 



6 Gravity 



7 Laws _ . 



3-9 



3-5 



3-6 

 0-37 



34 

 0-38 



0-33 



3-4 

 0-28 



0-23 







2-8 

 0-20 



8 Ward&Sloane. 







0-4 



0-4 



0-4 



0-4 



0-4 







0-18 



9 Bunsen Bichr._ 





0-27 





0-28 



0-26 



0-25 



022 





0-19 



0-15 



10 LeClanche 





1-18 



1-14 



1-10 



1-07 



099 



097 



093 





0-54 



11 LeClanche 





11 



1-2 



1-1 



1-2 



1-1 



1-2 





1-] 



0-9 



12 LeClanche 





1-0 



1-] 



1-1 





LI 



0-9 







0-5 



13 



LeClanche 





1-4 



1-4 



T4 



1-4 



1-4 



1-4 







1-0 



The results given in the table represent very fairly all that 

 we have obtained. The value of the resistance of a cell obtained 



Note. — Cells 1, 5, 6, 8 and 9 were of gallon size; the jars of the others would hold 

 about 3 pints each. The zinc of each Daniell cell was immersed in a solution of 

 zinc sulphate. The density of this solution in the case of cell 3 was 41° B. and 

 that of the solution of copper sulphate in the same cell was 21° B. In No. 4, 

 the density of each solution was 15° B. In cell 9 the zinc was immersed in a 

 mixture of 1 part of sulphuric acid, and 20 parts of water, and the carbon in 1 

 part of potassium bichromate, 2 parts of sulphuric acid, and 10 parts of water. 



The Hartmann & Braun bridge used for most of the measurements with alter- 

 nating currents has a resistance of 1-56 ohms in the bridge wire, 34 ohms in the 

 secondary coil of the inductive apparatus and 17 '5 ohms in the telephone. With 

 the pointer at the middle of the bridge-wire and the 1 ohm plug out, the resist- 

 ance in the bridge between the points where in measuring the resistances of a 

 battery its poles would be attached is 2-5 ohms. When the 10 ohm plug is. out 

 this resistance is 11 "3 ohms. Another bridge by the same makers gave indica- 

 tions practically identical with those of the first bridge. 



