EMF, Internal Resistance and Terminal Potential Differences of cell

A simple device to maintain a steady current in an electric circuit is the electrolytic cell.

A cell has two electrodes, called the positive (P) and the negative (N), as shown in Fig. 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 ε.

Thus ε = V₊+V_– > 0.) Note that ε is, actually, a potential difference and not a force.

Consider a resistor R connected across the cell. A current I flows across R from C to D.

The electrolyte through which a current flows has a finite resistance r, called the internal resistance. Consider first 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

= ε

Thus, emf ε 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 _– – Ir

= ε – I r

Note the negative sign in the expression (I r) for the potential difference between A and B. This is because the current I flows from B to A in the electrolyte.

We also observe that since V is the potential difference across R, we

V = I R

Combining Eqs.

The maximum current that can be drawn from a cell is for R = 0 and it is I max = ε/r. However, in most cells the maximum allowed current is much lower than this to prevent permanent damage to the cell.