We have already mentioned that a simple device to maintain a steady current in an electric circuit is the electrolytic cell. Basically a cell has two electrodes, called the positive (P) and the negative (N), as shown in Fig. 3.12. They are immersed in an electrolytic solution. Dipped in the solution, the electrodes exchange charges with the electrolyte. The positive electrode has a potential difference V (V > 0) between itself and the electrolyte solution immediately adjacent to it marked A in the figure. Similarly, the negative electrode develops a negative potential –(V )(V ≥ 0) relative to the electrolyte adjacent to it, marked as B in the figure. When there is no current, the electrolyte has the same potential throughout, so that the potential difference between P and N is V – (–V ) = V + V . This difference is called the electromotive force (emf) of the cell and is denoted by e. Thus e = V + V > 0. Note that e is, actually, a potential difference and not a force. The name emf, however, is used because of historical reasons, and was given at a time when the phenomenon was not understood properly.

To understand the significance of e, consider a resistor R connected across the cell (Fig. 3.12). A current I flows across R from C to D. As explained before, a steady current is maintained because current flows from N to P through the electrolyte. Clearly, across the electrolyte the same current flows but from N to P, whereas through R, it flows from P to N. The electrolyte through which a current flows has a finite resistance r, called the internal resistance. Consider first the situation when R is infinite so that I = V / R = 0, where V is the potential difference between P and N. Now, V = Potential difference between P and A + Potential difference between A and B + Potential difference between B and N = e.

If however R is finite, I is not zero. In that case the potential difference between P and N is V = V + V – I r = e – I r. Note the negative sign in the expression (Ir) for the potential difference between A and B. This is because the current I flows from B to A in the electrolyte. In practical calculations, internal resistances of cells in the circuit may be neglected when the current I is such that e >> I r. The actual values of the internal resistances of cells vary from cell to cell. The internal resistance of dry cells, however, is much higher than the common electrolytic cells.

We also observe that since V is the potential difference across R, we have from Ohm’s law V = IR. Combining Eqs. (3.38) and (3.39), we get I R = e – I r. Or, I= e / (R + r). The maximum current that can be drawn from a cell is for R = 0 and it is I_max = e/r. However, in most cells the maximum allowed current is much lower than this to prevent permanent damage to the cell.