The voltage between points A and B should equal the e.m.f. of the cell less the fall of potential inside the cell. But the strength of the current in the circuit equals
I = 3E/3r = E/r
where E is the e.m.f of the battery and r is its internal resistance. Consequently in our example the voltage between points A and B will be E - Ir = E - E = 0. Thus a voltmeter connected at points A and B will register zero.
The result we have obtained can be explained in the following way: If the terminals of one battery are short-circuited (i.e, if they are connected by a conductor of infinitely low resistance) the internal fall of potential will equal the battery's e.m.f and the potential at the battery's terminals will be zero. The circuit under consideration presents a similar picture. Here three identical
220 SOLUTIONS
batteries are connected in series by wires of infinitely low resistance, which is exactly similar to short-circuiting each battery. Therefore the potential at the terminals of each battery equals zero.
Clearly the reading of the voltmeter will not be altered by increasing the number of batteries, if the voltmeter still be connected at points A and B.