Potential dividers (4.3.3)
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A potential divider circuit is used to vary the potential difference (p.d.) output , connected to a fixed potential difference input A simple potential divider circuit consists of two resistors in series.
A potential divider is used to supply an external circuit with any p.d. between zero and the p.d supplied by the power source,

Kirchhoff’s second law states that the total p.d. supplied by the power source equals the sum of the p.d. across each resistor.
The resistances of the resistors determine the p.d. output. The resistor with the larger share of the total resistance receives a greater share of the total p.d.
A potential divider is used to split the potential difference of a power supply, but in some applications, the output voltage needs to vary.
The output voltage of a potential divider can be varied by replacing one of the fixed resistors with a variable resistor. As the resistance of the variable resistor changes, so does its share of the input p.d. causing to change in response.

Thermistors can be used as one of the resistors in a potential divider circuit, in order to provide a that varies with temperature input. This circuit could form part of a temperature sensor.
The resistance of a thermistor varies with its temperature:
- The higher the temperature of a thermistor, the lower its resistance.
- A higher temperature excites charge carriers in the thermistor, reducing the resistance.

When the temperature increases, the thermistor’s resistance drops. This results in the thermistor receiving a smaller fraction of the input voltage leading to a decrease in the output voltage Conversely, will rise when the temperature decreases.
A light-dependent resistor (LDR) can also be used as part of a potential divider circuit to provide an output voltage that varies in proportion to the intensity of the light. For example, an LDR could form part of a light sensor.
The resistance of a light-dependent resistor (LDR) varies with the light intensity incident on it:
- The higher the light intensity incident on an LDR, the lower its resistance.
- Incident light (of a sufficiently high frequency) excites charge carriers in an LDR, thereby reducing the resistance.

When light intensity is high, the LDR’s resistance is low. Consequently, it receives a smaller fraction of the input voltage resulting in a decrease in the output voltage Conversely, when the light intensity is low, the output voltage will increase.
Circuits with a low that require a varying may use a potentiometer instead of two separate fixed resistors. A potentiometer consists of three terminals and a sliding contact.
The position of the contact determines how the p.d. is shared between the two terminals and therefore the value of

As the slider is moved down, becomes smaller and becomes larger. now has a smaller share of the overall resistance and receives a smaller share of the overall voltage, resulting in a decrease in The inverse will happen if the slider is moved up.
An example of this type of circuit would be a sound volume control. Adjusting the sliding contact on the volume control changes the share of resistance and, therefore, the voltage output. The output would be connected to a speaker whose volume would change in response to the voltage level.
The voltage out for a potential divider circuit can be found using:
Where:
- is the resistance of resistor 1 measured in ohms.
- is the resistance of resistor 2 measured in ohms and this is the resistor where is measured.
- is the voltage across both resistors supplied by a power supply, measured in volts.
The potential divider equation is derived starting with Kirchhoff’s first law. For a potential divider circuit with fixed resistors and Kirchhoff’s first law states that the current is the same through both resistors.
Using Ohm’s law, the p.d. across resistor and (R_2\) respectively is:
These expressions show that the ratio of to is the ratio of the resistances:
is equal to the sum of the p.d. across each resistor, while is equal to the p.d. across resistor
The ratio of to is therefore:




