Internal Resistance

As noted before, a 12-V truck battery is physically larger, contains more charge and energy, and can deliver a larger current than a 12-V motorcycle battery. Both are lead-acid batteries with identical emf, but, because of its size, the truck battery has a smaller internal resistance \(r\). Internal resistance is the inherent resistance to the flow of current within the source itself.

This figure is a schematic representation of the two fundamental parts of any voltage source. The emf (represented by a script E in the figure) and internal resistance \(r\) are in series. The smaller the internal resistance for a given emf, the more current and the more power the source can supply.

This diagram shows a battery with a schematic indicating the e m f, represented by script E, and the internal resistance r of the battery. The voltage output of the battery is measured between the input and output terminals and is equal to the e m f minus the product of the current and the internal resistance.

Any voltage source (in this case, a carbon-zinc dry cell) has an emf related to its source of potential difference, and an internal resistance \(r\) related to its construction. (Note that the script E stands for emf.). Also shown are the output terminals across which the terminal voltage \(V\) is measured. Since \(V=\text{emf}-\text{Ir}\), terminal voltage equals emf only if there is no current flowing.

The internal resistance \(r\) can behave in complex ways. As noted, \(r\) increases as a battery is depleted. But internal resistance may also depend on the magnitude and direction of the current through a voltage source, its temperature, and even its history. The internal resistance of rechargeable nickel-cadmium cells, for example, depends on how many times and how deeply they have been depleted.

Things Great and Small: The Submicroscopic Origin of Battery Potential

Various types of batteries are available, with emfs determined by the combination of chemicals involved. We can view this as a molecular reaction (what much of chemistry is about) that separates charge.

The lead-acid battery used in cars and other vehicles is one of the most common types. A single cell (one of six) of this battery is seen in this figure. The cathode (positive) terminal of the cell is connected to a lead oxide plate, while the anode (negative) terminal is connected to a lead plate. Both plates are immersed in sulfuric acid, the electrolyte for the system.

A simplified view of a battery shows a rectangular container of sulfuric acid with two thin upright metal plates immersed in it, one made of lead and the other made of lead oxide. Each plate projects above the liquid line, providing a positive or negative terminal above the battery. The positive terminal is labeled as the cathode, and the negative terminal is labeled as the anode.

Artist’s conception of a lead-acid cell. Chemical reactions in a lead-acid cell separate charge, sending negative charge to the anode, which is connected to the lead plates. The lead oxide plates are connected to the positive or cathode terminal of the cell. Sulfuric acid conducts the charge as well as participating in the chemical reaction.

The details of the chemical reaction are left to the reader to pursue in a chemistry text, but their results at the molecular level help explain the potential created by the battery. This figure shows the result of a single chemical reaction. Two electrons are placed on the anode, making it negative, provided that the cathode supplied two electrons. This leaves the cathode positively charged, because it has lost two electrons. In short, a separation of charge has been driven by a chemical reaction.

Note that the reaction will not take place unless there is a complete circuit to allow two electrons to be supplied to the cathode. Under many circumstances, these electrons come from the anode, flow through a resistance, and return to the cathode. Note also that since the chemical reactions involve substances with resistance, it is not possible to create the emf without an internal resistance.

The diagram shows a simplified view of a battery depicting a rectangular container containing two thin upright metal plates immersed in a liquid. An enlarged view of the metal plates is also shown. One plate has positive charges on it shown as small spheres enclosing a positive sign. The other plate has negative charge on it shown as small spheres enclosing an electron. The electrons are shown to move from the positive plate to the negative plate using arrows through a molecular reaction in the liquid.

Artist’s conception of two electrons being forced onto the anode of a cell and two electrons being removed from the cathode of the cell. The chemical reaction in a lead-acid battery places two electrons on the anode and removes two from the cathode. It requires a closed circuit to proceed, since the two electrons must be supplied to the cathode.

Why are the chemicals able to produce a unique potential difference? Quantum mechanical descriptions of molecules, which take into account the types of atoms and numbers of electrons in them, are able to predict the energy states they can have and the energies of reactions between them.

In the case of a lead-acid battery, an energy of 2 eV is given to each electron sent to the anode. Voltage is defined as the electrical potential energy divided by charge: \(V=\cfrac{{P}_{\text{E}}}{q}\). An electron volt is the energy given to a single electron by a voltage of 1 V. So the voltage here is 2 V, since 2 eV is given to each electron. It is the energy produced in each molecular reaction that produces the voltage. A different reaction produces a different energy and, hence, a different voltage.

Internal Resistance

Internal Resistance

Things Great and Small: The Submicroscopic Origin of Battery Potential

Track Your Learning Progress