Batteries and Internal Resistance
Figure 4. A real cell with internal resistance.
A real battery has internal resistance, r, which lowers the voltage when the cell is connect to a load. If you try to send too much current through a battery, the internal resistance will convert the battery’s own chemical potential energy into thermal energy. The battery will get warm and electrons will leave the negative electrode with relatively little energy.
Figure 5. A cell with internal resistance in series with a load, R.
The EMF of the battery is given by E and represents the voltage when the battery is open circuit. If the battery had no internal resistance, the current flowing in the circuit would be given by Ohm’s law, I =E/R where R is the resistance of the load.
The internal resistance adds to the total resistance of the circuit. If we call the new total resistance of the cell and load,
Req = r + R
Then current is then I= E/Req = E/(r + R).(3)
Since Req is larger than R the current flowing in the circuit is reduced. Therefore, if we are making a cell we want the internal resistance to be a small as possible.
What is the voltage across the resistor R? Clearly it is not the same as the EMF because of the internal resistance. We know that the EMF, E = Ir + IR. We also know that the voltage across the resistor R is IR. Rearranging these two equations we find the voltage in terms of E, r and R.
V = E – Ir (4).
This equation also shows that if we draw a lot of current from the circuit we see the voltage reduces. A good example of this is a car starting with its lights switched on. When the ignitioin key is turned, the electric starter-motor uses a lot of current before it starts to turn. The current for this is supplied by the car battery, which also powers the lights. The voltage available for the lights is reduced at this moment and the lights dim as the car starts. They quickly become bright again once the engine is turning over because less current is required by the starter motor. (When the car has started no current is drawn by the starter motor because it disengages from the engine.)
Table 1. Metal Reactivity Series from most reactive to least reactive.