MUTUAL INDUCTION AND THE INTERNAL RESISTANCE OF A 
VOLTAIC CELL. 
BY L. BEGEMAN. 
The usual method of making a rapid determination of the internal 
resistance of a voltiac cell, primary or secondary, is by means of the 
condenser in circuit with a ballistic galvanometer. The deflection of the 
galvanometer due to the discharge of the condenser is first taken on 
open circuit with the cell and again when the cell is on a closed circuit 
the known resistance. The working formula is r=d — d^ over d^XR, in 
which d and d^ are the different deflections of the galvanometer needle 
and R is the external resistance of the closed circuit. The explanation 
of this method can be found in Carhart and Patterson’s Electrical Meas- 
urements. Not having a good standard condenser it occurred to me 
some time ago while working with a number of students in electrical 
measurements that an induction coil might be substituted for a con- 
denser in such determinations. The idea appealed to me particularly 
as I thought that such a method might indirectly bring the student to 
a definite, elementary understanding of the terms self induction and 
mutual induction. Every one who has ever attempted to teach these con- 
ceptions to a class of students in secondary work, possessing as they 
usually do an inadequate mathematical training, must realize the diffi- 
culty of the task. And yet in view of the general commercial use of 
periodic currents at the present time, it becomes quite necessary to pay 
some attention to these phenomena in a practical way. 
The diagrammatic sketch below. Figure 1, represents the arrange- 
ment of the apparatus for the determination of the internal resistance 
of a primary or secondary cell by means of an induction coil. In my 
work I used a small induction coil like that found in the ordinary tele- 
phone transmitter. 
The mutual induction of the coil under the action of a current of one 
tenth of an ampere was approximately 30 millihenrys. In the diagram 
I is the induction coil, G is the galvanometer in the secondary circuit. 
The galvanometer should be ballistic although type H D’arsonval made 
by Leeds, Northrup & Co. gave very good results. The primary circuit 
contains a resistance box R, a battery B and a key ; preferably a knife 
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