Potential divider

A potential divider uses resistors connected in series across a power supply to produce an output potential difference that is a fraction of the supply potential difference. The output is measured across one part of the series circuit.

The same current flows through each series resistor. A larger resistance therefore has a larger potential difference across it: the supply potential difference is divided between the resistors in proportion to their resistances.

Potential divider with two resistors

Suppose two resistors, $$$R_1$$$ and $$$R_2$$$ , are connected in series across a supply of potential difference $V_{\text{in}}$ . If the output is measured across $$$R_2$$$ , it is:

V_{\text{out}} = V_{\text{in}}\frac{R_2}{R_1+R_2}

The fraction is the resistance across which the output is measured divided by the total series resistance. For example, if the two resistances are equal, the output across either resistor is half the supply potential difference.

With a constant supply and fixed resistances, the output is constant. Changing either resistance changes the fraction of the supply across $$$R_2$$$ . These relationships assume that the output draws negligible current, so that the current through the two resistors is effectively the same.

Adjustable and sensor-based potential dividers

A variable resistor allows the resistance to be changed, providing an adjustable output. In a sliding-contact variable resistor, the contact selects a point along a resistive track connected across the supply. Moving the contact changes the resistance on each side of it, allowing the output to be adjusted continuously from one end of the supply range to the other.

A potential divider can also use a sensor whose resistance changes with its surroundings:

An NTC thermistor has a resistance that decreases as its temperature rises.
An LDR has a resistance that decreases as light intensity increases.

Whether the output rises or falls depends on where it is measured. If the output is across the sensor, a decrease in the sensor’s resistance decreases the output. If the output is across the other, fixed resistor, the same decrease in sensor resistance increases the output. Thus, either arrangement can be chosen according to how the output needs to respond.