Potential Differences in a Circuit with an EMF Source
The graphic shows the potential rises and falls in a circuit with a battery providing a source of electromotive force (EMF) of magnitude . The circuit contains a resistance , as well as an internal resistance . The associated changes in the potential add to , when a current passes through the points (before the EMF source) and (before the resistance) and back to , with corresponding voltages and . These changes in the potential, when summed algebraically, must be equal to zero, by Kirchhoff's second rule.
The following conditions hold for the potential differences in the circuit: and .
For a detailed exposition, see D. Halliday, R. Resnick, and K. S. Krane, Physics, Vol. 2, 5th ed., New York: Wiley, 2001.