What is a potential divider?

A potential divider is two or more resistors connected in series across a fixed supply, with the output taken across one of them, so that only part of the supply potential difference appears at the output.

State the potential divider relationship in ratio form.

The potential differences are in the same ratio as the resistances, so V₁/V₂ = R₁/R₂ for two resistors in series.

Explain why the supply potential difference divides between two series resistors in proportion to their resistances.

The same current passes through both resistors, so the potential difference across each is IR and is therefore directly proportional to that resistor's resistance.

A 12 V supply is connected across a 3.0 kΩ resistor in series with a 1.0 kΩ resistor. Calculate the potential difference across the 1.0 kΩ resistor.

The output is 12 × 1.0 ÷ 4.0 = 3.0 V, and the remaining 9.0 V across the 3.0 kΩ resistor is three times as large, as the 3:1 resistance ratio requires.

A 4.7 kΩ resistor is connected in series with a second resistor across a 12 V supply. Calculate the resistance needed for the output across the second resistor to be 5.0 V.

Since R₂/(4700 + R₂) = 5.0/12, we get 12R₂ = 23 500 + 5R₂, so R₂ = 3.4 kΩ, and 12 × 3357 ÷ (4700 + 3357) = 5.0 V confirms the result.

CCEA A-Level Physics 1210

Physical Quantities, Scalars and Vectors

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Linear Motion and Dynamics

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Current, Charge and Potential Difference

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Resistance and Resistivity

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Internal Resistance and Potential Dividers

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Internal Resistance and Potential Dividers

The potential divider and variable output

3 things to know
Unit AS 1

Overview

Recall questions on what a potential divider is, the divider equation and its ratio form, why the supply voltage divides in proportion to the resistances, using a single variable resistor as a divider, the advantage over a series variable resistor, worked calculations, and the effect of scaling both resistances together.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Why does the choice of resistance values in a potential divider matter for a battery-powered circuit?

Key term

Why is a potential divider used rather than a series variable resistor when setting the operating point of a sensing circuit?

Key term

State the potential divider equation for two resistors and define every symbol.

Questions from this subtopic

Each one with the model answer underneath.

1
What is a potential divider?
Model answer
A potential divider is two or more resistors connected in series across a fixed supply, with the output taken across one of them, so that only part of the supply potential difference appears at the output.
2
State the potential divider equation for two resistors and define every symbol.
Model answer
The output is Vₒᵤₜ = Vᵢₙ × R₂/(R₁ + R₂), where Vᵢₙ is the supply potential difference in volts, R₂ the resistance in ohms of the resistor across which the output is taken and R₁ the resistance in ohms of the other resistor.
3
State the potential divider relationship in ratio form.
Model answer
The potential differences are in the same ratio as the resistances, so V₁/V₂ = R₁/R₂ for two resistors in series.
4
Explain why the supply potential difference divides between two series resistors in proportion to their resistances.
Model answer
The same current passes through both resistors, so the potential difference across each is IR and is therefore directly proportional to that resistor's resistance.
5
A 12 V supply is connected across a 3.0 kΩ resistor in series with a 1.0 kΩ resistor. Calculate the potential difference across the 1.0 kΩ resistor.
Model answer
The output is 12 × 1.0 ÷ 4.0 = 3.0 V, and the remaining 9.0 V across the 3.0 kΩ resistor is three times as large, as the 3:1 resistance ratio requires.
6
A 4.7 kΩ resistor is connected in series with a second resistor across a 12 V supply. Calculate the resistance needed for the output across the second resistor to be 5.0 V.
Model answer
Since R₂/(4700 + R₂) = 5.0/12, we get 12R₂ = 23 500 + 5R₂, so R₂ = 3.4 kΩ, and 12 × 3357 ÷ (4700 + 3357) = 5.0 V confirms the result.

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