contents

Physics

3.11 - Potential Dividers

6 min

note 1 of 7

A potential divider shares a voltage between two resistors

A potential divider is a circuit that splits a supply voltage between two resistors in series.
It allows a circuit to take a smaller voltage from a larger supply.
The supply's potential difference is shared between the two resistors in the ratio of their resistances: the larger a resistor's share of the total resistance, the larger its share of the voltage.

Because the same current passes through both resistors in series, a larger resistance has a larger potential difference across it.

Worked through with numbers

A 9 V supply is connected across a 2 Ω resistor and a 1 Ω resistor in series, as shown in the circuit below.

Total resistance = 2 + 1 = 3 Ω.
The 2 Ω resistor takes 2/3 of the supply: 2/3 of 9 V = 6 V.
The 1 Ω resistor takes 1/3 of the supply: 1/3 of 9 V = 3 V.
The two shares add up to the 9 V supply.

A battery labelled 9 V connected across two resistors in series, R1 = 1 Ω with a voltmeter reading 3 V across it, and R2 = 2 Ω with a voltmeter reading 6 V.

note 2 of 7

The potential-divider ratio equation

For two resistors in a potential divider, the ratio of the resistances equals the ratio of the potential differences across them.

Ratio equation

$\frac{R_{1}}{R_{2}} = \frac{V_{1}}{V_{2}}$

Where:

$R_{1}, R_{2}$ = The two resistances, in ohms (Ω)
$V_{1}, V_{2}$ = The potential differences across $R_{1}$ and $R_{2}$ , in volts (V)

The two potential differences always add up to the supply: $V_{s o u r c e} = V_{1} + V_{2}$ .

note 3 of 7

Worked example - Using the ratio equation

A potential divider has a 15 V supply. $R_{1}$ is 25 Ω and $R_{2}$ is 50 Ω, and a voltmeter reads 5 V across $R_{1}$ . Use the ratio equation to find the potential difference across $R_{2}$ .

Step 1 - Write down the ratio equation

$\frac{V_{1}}{V_{2}} = \frac{R_{1}}{R_{2}}$

Step 2 - Rearrange and substitute to find V₂

$V_{2} = V_{1} \times \frac{R_{2}}{R_{1}} = 5 \times \frac{50}{25} = 10 V$

The potential difference across $R_{2}$ is 10 V.

The two shares add up to the supply: $V_{1} + V_{2} = 5 + 10 = 15 V$ .

note 4 of 7

Varying the output with a variable resistor

Replacing one fixed resistor with a variable resistor lets the output voltage be adjusted while the circuit runs.

With the variable resistor set to zero, almost the whole supply voltage appears across the fixed resistor, so the output is close to the full supply.
As the variable resistance increases, it takes a larger share of the supply, and the output across the fixed resistor falls.

A battery labelled V supply in a loop with a fixed resistor and a variable resistor in series, dashed lines marking V output taken across the fixed resistor.

note 5 of 7

The output voltage formula

$V_{2} = (\frac{R_{2}}{R_{1} + R_{2}}) V_{s}$

Where:

$V_{2}$ = The output potential difference across $R_{2}$ , in volts (V)
$R_{1}, R_{2}$ = The two resistances, in ohms (Ω)
$V_{s}$ = The supply potential difference, in volts (V)

The output depends on the relative sizes of the resistors:

If $R_{2}$ is much larger than $R_{1}$ , the output is close to the full supply voltage.
If $R_{2}$ is much smaller than $R_{1}$ , the output is close to zero.

note 6 of 7

Worked example - Finding the output voltage

A potential divider has a 15 V supply. $R_{1}$ is 25 Ω and $R_{2}$ is 50 Ω. A device is connected across $R_{2}$ . What output voltage does it receive?

Step 1 - Write down the values

$V_{s}$ = 15 V, $R_{1}$ = 25 Ω, $R_{2}$ = 50 Ω.

Step 2 - Substitute into the output voltage equation

$\begin{matrix} V_{2} & = (\frac{R_{2}}{R_{1} + R_{2}}) V_{s} \\ = (\frac{50}{25 + 50}) \times 15 \\ = 10 V \end{matrix}$

The device receives an output of 10 V.

note 7 of 7

Sensing circuits with an LDR or thermistor

A potential divider becomes a sensing circuit when one resistor is replaced by a component whose resistance changes with its surroundings:
- Thermistor - Resistance changes with temperature.
- Light-dependent resistor (LDR) - Resistance changes with light level.
The output voltage then changes automatically with the conditions.

Example - A temperature-controlled fan

A thermistor is placed in series with a fixed resistor, and a fan is connected across the fixed resistor.

As the room warms up, the thermistor's resistance falls, so it takes a smaller share of the supply voltage.
The voltage across the fixed resistor (and the fan) rises, so the fan runs faster.

A battery labelled V supply in a loop with a fixed resistor and a thermistor in series, and a motor symbol labelled fan connected across the fixed resistor.

Replacing the thermistor with an LDR gives a circuit that responds to light instead of temperature in the same way.

key terms

TermDefinition

Potential dividerA circuit that splits a supply voltage between two resistors in series.

Sensing circuitA potential divider containing a component whose resistance changes with its surroundings (such as light or temperature), so the output voltage changes too.

end of notes

Key points to remember

Take a quiz View flashcards

3.12 - TransistorsNext up

contents

Physics

3.11 - Potential Dividers

6 min

note 1 of 7

A potential divider shares a voltage between two resistors

A potential divider is a circuit that splits a supply voltage between two resistors in series.
It allows a circuit to take a smaller voltage from a larger supply.
The supply's potential difference is shared between the two resistors in the ratio of their resistances: the larger a resistor's share of the total resistance, the larger its share of the voltage.

Because the same current passes through both resistors in series, a larger resistance has a larger potential difference across it.

Worked through with numbers

A 9 V supply is connected across a 2 Ω resistor and a 1 Ω resistor in series, as shown in the circuit below.

Total resistance = 2 + 1 = 3 Ω.
The 2 Ω resistor takes 2/3 of the supply: 2/3 of 9 V = 6 V.
The 1 Ω resistor takes 1/3 of the supply: 1/3 of 9 V = 3 V.
The two shares add up to the 9 V supply.

note 2 of 7

The potential-divider ratio equation

For two resistors in a potential divider, the ratio of the resistances equals the ratio of the potential differences across them.

Ratio equation

$\frac{R_{1}}{R_{2}} = \frac{V_{1}}{V_{2}}$

Where:

$R_{1}, R_{2}$ = The two resistances, in ohms (Ω)
$V_{1}, V_{2}$ = The potential differences across $R_{1}$ and $R_{2}$ , in volts (V)

The two potential differences always add up to the supply: $V_{s o u r c e} = V_{1} + V_{2}$ .

note 3 of 7

Worked example - Using the ratio equation

A potential divider has a 15 V supply. $R_{1}$ is 25 Ω and $R_{2}$ is 50 Ω, and a voltmeter reads 5 V across $R_{1}$ . Use the ratio equation to find the potential difference across $R_{2}$ .

Step 1 - Write down the ratio equation

$\frac{V_{1}}{V_{2}} = \frac{R_{1}}{R_{2}}$

Step 2 - Rearrange and substitute to find V₂

$V_{2} = V_{1} \times \frac{R_{2}}{R_{1}} = 5 \times \frac{50}{25} = 10 V$

The potential difference across $R_{2}$ is 10 V.

The two shares add up to the supply: $V_{1} + V_{2} = 5 + 10 = 15 V$ .

note 4 of 7

Varying the output with a variable resistor

Replacing one fixed resistor with a variable resistor lets the output voltage be adjusted while the circuit runs.

With the variable resistor set to zero, almost the whole supply voltage appears across the fixed resistor, so the output is close to the full supply.
As the variable resistance increases, it takes a larger share of the supply, and the output across the fixed resistor falls.

note 5 of 7

The output voltage formula

$V_{2} = (\frac{R_{2}}{R_{1} + R_{2}}) V_{s}$

Where:

$V_{2}$ = The output potential difference across $R_{2}$ , in volts (V)
$R_{1}, R_{2}$ = The two resistances, in ohms (Ω)
$V_{s}$ = The supply potential difference, in volts (V)

The output depends on the relative sizes of the resistors:

If $R_{2}$ is much larger than $R_{1}$ , the output is close to the full supply voltage.
If $R_{2}$ is much smaller than $R_{1}$ , the output is close to zero.

note 6 of 7

Worked example - Finding the output voltage

A potential divider has a 15 V supply. $R_{1}$ is 25 Ω and $R_{2}$ is 50 Ω. A device is connected across $R_{2}$ . What output voltage does it receive?

Step 1 - Write down the values

$V_{s}$ = 15 V, $R_{1}$ = 25 Ω, $R_{2}$ = 50 Ω.

Step 2 - Substitute into the output voltage equation

$\begin{matrix} V_{2} & = (\frac{R_{2}}{R_{1} + R_{2}}) V_{s} \\ = (\frac{50}{25 + 50}) \times 15 \\ = 10 V \end{matrix}$

The device receives an output of 10 V.

note 7 of 7

Sensing circuits with an LDR or thermistor

A potential divider becomes a sensing circuit when one resistor is replaced by a component whose resistance changes with its surroundings:
- Thermistor - Resistance changes with temperature.
- Light-dependent resistor (LDR) - Resistance changes with light level.
The output voltage then changes automatically with the conditions.

Example - A temperature-controlled fan

A thermistor is placed in series with a fixed resistor, and a fan is connected across the fixed resistor.

As the room warms up, the thermistor's resistance falls, so it takes a smaller share of the supply voltage.
The voltage across the fixed resistor (and the fan) rises, so the fan runs faster.

Replacing the thermistor with an LDR gives a circuit that responds to light instead of temperature in the same way.

key terms

TermDefinition

Potential dividerA circuit that splits a supply voltage between two resistors in series.

Sensing circuitA potential divider containing a component whose resistance changes with its surroundings (such as light or temperature), so the output voltage changes too.

end of notes

Key points to remember

Take a quiz View flashcards

3.12 - TransistorsNext up

3.11 - Potential Dividers

A potential divider shares a voltage between two resistors

Worked through with numbers

The potential-divider ratio equation

Ratio equation

Where:

Worked example - Using the ratio equation

Step 1 - Write down the ratio equation

Step 2 - Rearrange and substitute to find V2

Varying the output with a variable resistor

The output voltage formula

Where:

The output depends on the relative sizes of the resistors:

Worked example - Finding the output voltage

Step 1 - Write down the values

Step 2 - Substitute into the output voltage equation

Sensing circuits with an LDR or thermistor

Example - A temperature-controlled fan

Key points to remember

3.11 - Potential Dividers

A potential divider shares a voltage between two resistors

Worked through with numbers

The potential-divider ratio equation

Ratio equation

Where:

Worked example - Using the ratio equation

Step 1 - Write down the ratio equation

Step 2 - Rearrange and substitute to find V2

Varying the output with a variable resistor

The output voltage formula

Where:

The output depends on the relative sizes of the resistors:

Worked example - Finding the output voltage

Step 1 - Write down the values

Step 2 - Substitute into the output voltage equation

Sensing circuits with an LDR or thermistor

Example - A temperature-controlled fan

Key points to remember

Step 2 - Rearrange and substitute to find V₂

Step 2 - Rearrange and substitute to find V₂