Potential Divider Circuits (AQA A Level Physics): Revision Note

Potential divider circuit

• When two resistors are connected in series, through Kirchhoff’s second law, the potential difference across the power source is divided between them

• Potential dividers are circuits which produce an output voltage as a fraction of its input voltage

• Potential dividers have three main purposes:

  • To provide a variable potential difference

  • To enable a specific potential difference to be chosen

  • To split the potential difference of a power source between two or more components

• Potential dividers are used widely in volume controls and sensory circuits using LDRs and thermistors

• Potential divider circuits are based on the ratio of voltage between components

  • This is equal to the ratio of the resistances of the resistors in the diagram below, giving the following equation:

• Where:

  • $R_2$ is the numerator and the resistance of the resistor over $V_{out}$

  • $R_1$ is the other resistance in series

  • $V_{out}$ is the output potential difference

  • $V_{in}$ is the input potential difference

• The potential divider equation can also be written:

$V_{out}=\frac{R_1}{R_1+R_2}{V}_{in}$

• Where this time:

  • $R_1$ is the numerator and the resistance of the resistor over $V_{out}$

  • $R_2$ is the other resistance in series

• Either notation will give the same answer

  • The numerator has to be the resistance of the resistor over $V_{out}$

• In the circuit shown above:

  • The input voltage $V_{in}$ is applied to the top and bottom of the series resistors

  • The output voltage $V_{out}$ is measured from the centre to the bottom of resistor $R_2$

• The potential difference $V$ across each resistor depends upon its resistance $R$:

  • The resistor with the largest resistance will have a greater potential difference than the other one from $V=IR$

  • If the resistance of one of the resistors is increased, it will get a greater share of the potential difference, whilst the other resistor will get a smaller share

• In potential divider circuits, the p.d across a component is proportional to its resistance from $V=IR$

Variable resistance components

• Variable and sensory resistors are used in potential dividers to vary the output voltage

  • This could cause an external component to switch on or off e.g. a heater switching off automatically when its surroundings are at room temperature

• Sensory resistors used are Light Dependent Resistors (LDRs) and thermistors

• The voltmeter in both circuits is measuring $V_{out}$

• Recall that the resistance of an LDR varies with light intensity

  • The higher the light intensity, the lower the resistance and vice versa

• An LDR circuit is often used for street and security lights

• The resistance of a thermistor varies with temperature

  • The hotter the thermistor, the lower the resistance and vice versa

• A thermistor circuit is used in fire alarms, ovens and digital thermometers

• From Ohm’s law $V=IR$, the potential difference $V_{out}$ from a resistor in a potential divider circuit is proportional to its resistance

  • If an LDR or thermistor's resistance decreases, the potential difference through it also decreases

  • If an LDR or thermistor's resistance increases, the potential difference through it also increases

• Since the total p.d of the components must be equal to $V_{in}$, if the p.d of the sensory resistor decreases then the p.d of the other resistor in the circuit must increase and vice versa