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Physics 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 (3.36) + – Note that eis, actually, a potential difference and not a force. The name emf, however, is used because of historical reasons, and was givenatatimewhenthephenomenonwasnotunderstoodproperly. To understand the significance of e, consider a resistor R connected across the cell (Fig. 3.12). A current I flows across R FIGURE 3.12 (a) Sketch of from C to D. As explained before, a steady current is maintained an electrolyte cell with because current flows from N to P through the electrolyte. Clearly, positive terminal P and across the electrolyte the same current flows through the electrolyte negative terminal N. The but from N to P, whereas through R, it flows from P to N. gap between the electrodes The electrolyte through which a current flows has a finite is exaggerated for clarity. A and B are points in the resistance r, called the internal resistance. Consider first the situation when R is infinite so that I = V/R = 0, where V is the electrolyte typically close to potential difference between P and N. Now, P and N. (b) the symbol for a cell, + referring to P and V = Potential difference between P and A – referring to the N + Potential difference between A and B electrode. Electrical + Potential difference between B and N connections to the cell are = e (3.37) made at P and N. Thus, emf e is the potential difference between the positive and negative electrodes in an open circuit, i.e., when no current is flowing through the cell. 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 (3.38) 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 = I R (3.39) Combining Eqs. (3.38) and (3.39), we get 94 Reprint 2026-27