Potential dividers are useful but to explain them let us start with electric current. The current carries energy from the energy source (e.g. the battery or the generator) around the circuit. The current does not get used up it simply goes around and around. That is just like water in a central heating system carrying heat from the boiler and flowing back cold and then picking up more energy.
A voltmeter measures the change of energy of the electric current between one place and another, just as we might measure the change in temperature as water enters and leaves the radiator.
The potential difference or voltage we measure is the number of joules of energy transferred to the bulb, in the diagram above, by every coulomb of electricity.
If we had two radiators attached to our boiler, then the energy would be shared between them. The total energy is the same, it has just been divided into two parts.
Then, in a similar way, the energy of the electric current is divided by two resistors. The energy delivered is measured by the potential difference, hence the two resistors are a potential divider.
Using a potential divider
If the resistors are of different sizes then different amounts of energy are transferred in each (just as a big radiator emits more heat than a small one).
The potential difference, measured by the voltage, is divided up in exactly the same ratio as the size of the resistors. This is a useful idea in practical measuring circuits. It makes it easier to measure a change in the potential difference.
I =V1/R1 = V2/R2
and because V1/R1 = V2/R2 then rearranging this: V1/V2 = R1/R2 so the ratio of the resistances is the same as the ratio of the voltages.
For example a temperature change changes the resistance of a thermistor but the potential difference (voltage) across the thermistor in the circuit below would stay the same. The (tiny) current would alter but this is quite hard to measure.
In this circuit below a change in the resistance of the thermistor would alter the balance of voltages measured and these values would be much easier and therefore more accurate, to measure.
Rather than use two fixed resistors it is often more convenient to use one length of resistance material divided into two parts by a sliding contact. A range of PDs can be obtained - that is a potentiometer.
More convenient still if the resistance material is bent around and then the sliding contact can be on a spindle that is simply twisted around. So a commercial potentiometer looks like this. The centre connector is to the slide, turned by the control on the top.
So a commercial potentiometer looks like this. The centre connector is to the slide, turned by the control on the top.
The potentiometer is very commonly used in electrical machines to produce any PD up to the maximum of the supply.