Electromotive Force and Internal Resistance

A battery or cell is described as a source of electromotive force (emf), usually denoted $\varepsilon$. The name is, admittedly, something of a historical misnomer -- an emf is not literally a force at all, but a potential difference, measured in volts. Formally, the emf of a cell or battery is the potential difference it provides when no current at all is flowing in the external circuit (an open circuit); it is this emf that determines how much work the cell can do in moving a given amount of charge around a complete circuit.

For an idealised battery, with zero internal resistance, the terminal voltage (the potential difference actually measured across its terminals) is always exactly equal to its emf, no matter how much current is drawn. Real batteries are not ideal, however: because a real battery is physically made of electrodes and an electrolyte, there is an unavoidable resistance to the flow of charge WITHIN the battery itself, called its internal resistance, r. Because of r, a real battery's terminal voltage is generally NOT equal to its emf once current starts flowing -- and a freshly manufactured cell typically has a low internal resistance, which then gradually increases as the cell ages and its internal chemistry degrades. Measuring the emf directly requires connecting only a high-resistance voltmeter across the cell (with no external resistance in the cir …