Often we want to be able vary the voltage across a component – to dim the lights or turn the sound up or down for example. We can do this by varying the resistance in a circuit. The output voltage can be varied with a potential divider shown below. Changing the value of the variable resistor R2 changes the output voltage VOUT .
The total resistance in the circuit is
so if the battery voltage is
we can use Ohm's Law,
to get the current:
Now apply Ohm's law to the output resistor
to get the output voltage
If the output resistance R2 is reduced to zero, the output voltage is zero. VOUT can be increased to a maximum by increasing R2 to its largest possible value.
In practice a slightly different arrangement is often used with a sliding contact on a wire.
Resistance is proportional to length so