Engineering · Electrical engineering

Voltage divider with two series resistors

An unloaded voltage divider provides a fraction of its input voltage across the lower resistor R₂.

AdvancedUniversity/collegeBachelor foundationsSubject specialization

Create flashcards or a quiz I already have an account

Free to browse · flashcards or a multiple-choice quiz · import from Essential

Formula

U_{out} = U_{in} \frac{R _{2}}{R _{1} + R _{2}}

U in V; R in Ω

Variables & units

Variables & units
Symbol	Meaning	Unit
Uout	Output voltage across lower resistor R₂	V
$Uin$	Total input voltage across the series pair	V
R₁, R₂	Series resistors; output is measured across R₂	Ω

LaTeX

U_\mathrm{out}=U_\mathrm{in}\frac{R_2}{R_1+R_2}

QUANTA STUDYquanta-study.de

Derivation & background

The equation follows from the same current through both series resistors and Ohm’s law. It assumes an unloaded output; a connected load lies in parallel with R₂ and changes the division. At high resistance values, input and leakage currents can also matter. State polarity and output tap clearly.

Exam blueprint

Validity range

Derivation steps

An unloaded voltage divider provides a fraction of its input voltage across the lower resistor R₂.

1State the model assumptions and list quantities with units.
2Substitute into Uout = Uin·R₂/(R₁+R₂); convert quantities to SI first.
3For Uin=12 V, R₁=2 kΩ and R₂=1 kΩ, Uout=12·1/(2+1)=4 V.

Rearrangements

Base equation for the target quantity

U_\mathrm{out}=U_\mathrm{in}\frac{R_2}{R_1+R_2}

Preserve signs, boundary conditions and units when rearranging.

Task variant

Work through the numerical example for “Voltage divider with two series resistors” and check its unit and magnitude.

For Uin=12 V, R₁=2 kΩ and R₂=1 kΩ, Uout=12·1/(2+1)=4 V.

Common mistakes

Substituting a related quantity that shares the same symbol.

Use variable definitions and check: U in V; R in Ω.

Exam context

Create reference and measurement voltages from a known supply.

Formula cluster

Electrical engineering

An unloaded voltage divider provides a fraction of its input voltage across the lower resistor R₂.

Σ I hinein = Σ I hinaus; Σ ΔV = 0

Kirchhoff’s junction and loop rules

U = R·I

Ohm's Law

Rges = R₁+R₂ ; 1/Rges = 1/R₁+1/R₂

Resistors in Series and Parallel

Worked example

For Uin=12 V, R₁=2 kΩ and R₂=1 kΩ, Uout=12·1/(2+1)=4 V.

Applications

Create reference and measurement voltages from a known supply.

How do you calculate with Voltage divider with two series resistors?

Here is how to work through a typical Voltage divider with two series resistors (Uout = Uin·R₂/(R₁+R₂)) task step by step:

1
Task
Work through the numerical example for “Voltage divider with two series resistors” and check its unit and magnitude.
Solution path
For Uin=12 V, R₁=2 kΩ and R₂=1 kΩ, Uout=12·1/(2+1)=4 V.

Frequently asked questions about Voltage divider with two series resistors

Why is Uout measured across R₂?+

The chosen tap is between R₁ and R₂, with R₂ connected to the reference node. Voltage across R₂ is therefore the lower share of total series voltage. Across R₁, the numerator would instead be R₁. Always state the output tap and reference direction. The simple ratio assumes two series resistors and a high-impedance output measurement. Output is across R₂. A real load changes the effective lower resistance, while tolerance and source resistance shift the result; include them when accuracy matters. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.

What happens when a load is connected?+

A load RL at the output is in parallel with R₂. Replacing R₂ by R₂∥RL lowers the effective lower resistance and usually reduces Uout. The unloaded formula is a good approximation only when RL is much larger than R₂. Measurement-device impedance matters for accurate dividers. The simple ratio assumes two series resistors and a high-impedance output measurement. Output is across R₂. A real load changes the effective lower resistance, while tolerance and source resistance shift the result; include them when accuracy matters. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.

How should I choose the resistor ratio?+

For target ratio r=Uout/Uin, r=R₂/(R₁+R₂). Many resistor pairs give the same ratio but draw different current and load the source differently. Smaller resistors improve load robustness but increase power loss. Choose values based on source impedance, load and power too. The simple ratio assumes two series resistors and a high-impedance output measurement. Output is across R₂. A real load changes the effective lower resistance, while tolerance and source resistance shift the result; include them when accuracy matters. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.

How do I check the result and units for Voltage divider with two series resistors?+

Write the quantity and unit from the variable list next to every value: U in V; R in Ω. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For Uin=12 V, R₁=2 kΩ and R₂=1 kΩ, Uout=12·1/(2+1)=4 V. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. The simple ratio assumes two series resistors and a high-impedance output measurement. Output is across R₂. A real load changes the effective lower resistance, while tolerance and source resistance shift the result; include them when accuracy matters. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.

Which model limit matters for Voltage divider with two series resistors?+

The background states this starting condition: The equation follows from the same current through both series resistors and Ohm’s law. It assumes an unloaded. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. The simple ratio assumes two series resistors and a high-impedance output measurement. Output is across R₂. A real load changes the effective lower resistance, while tolerance and source resistance shift the result; include them when accuracy matters. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.

Quanta exam set

Curated exam set for "Voltage divider with two series resistors":

Question (front)

Which formula describes Voltage divider with two series resistors?

Answer in your set

Question (front)

How do you rearrange Voltage divider with two series resistors for Base equation for the target quantity?

Answer in your set

Question (front)

Which common mistake happens with Voltage divider with two series resistors?

Answer in your set

+ 7 more cards: units, variables, derivation, example, exam task

The formula set contains 10 cards. After importing, review them and start practicing; your ratings determine later review intervals.

Create flashcards or a quiz I already have an account

Subject references and further reading

This list names subject references and further reading. A page or section number appears when it is part of the reference; these are not verbatim quotations.

[1]OpenStax, University Physics Volume 2, voltage-divider circuit example.

More formulas: Electrical and control engineering

C(s)=K_P+\frac{K_I}{s}+K_Ds

Ideal PID controller transfer function

U_C(t)=U_0(1-e^{-t/(RC)}),\qquad \tau=RC

Time response of an RC charging circuit

i(t)=\frac{U_0}{R}(1-e^{-tR/L}),\qquad \tau=\frac{L}{R}

Current rise in an RL circuit

Z=\sqrt{R^2+(\omega L-1/(\omega C))^2}

Impedance of a series RLC circuit

Spaced-repetition apps

Compare scheduling workflows

Study evidence

Read methods, results and limits

Compare flashcard apps

FSRS support and study features

Create a formula exam set

From Essential in Quanta

Retain Voltage divider with two series resistors for exams

Create a curated FSRS exam set for Uout = Uin·R₂/(R₁+R₂): formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.

Create flashcards or a quiz Already registered? Continue directly

Curated formula set · LaTeX · FSRS spaced repetition · import from Essential

Quanta Study editorial team

Symbol

Meaning

Unit

Uout

Output voltage across lower resistor R₂

Uin

Total input voltage across the series pair

R₁, R₂

Series resistors; output is measured across R₂

Exam blueprint

Validity range

Derivation steps

An unloaded voltage divider provides a fraction of its input voltage across the lower resistor R₂.

1State the model assumptions and list quantities with units.
2Substitute into Uout = Uin·R₂/(R₁+R₂); convert quantities to SI first.
3For Uin=12 V, R₁=2 kΩ and R₂=1 kΩ, Uout=12·1/(2+1)=4 V.

How do you calculate with Voltage divider with two series resistors?

Here is how to work through a typical Voltage divider with two series resistors (Uout = Uin·R₂/(R₁+R₂)) task step by step:

Task

Work through the numerical example for “Voltage divider with two series resistors” and check its unit and magnitude.

Solution path

For Uin=12 V, R₁=2 kΩ and R₂=1 kΩ, Uout=12·1/(2+1)=4 V.

Frequently asked questions about Voltage divider with two series resistors

Why is Uout measured across R₂?+

What happens when a load is connected?+

How should I choose the resistor ratio?+

How do I check the result and units for Voltage divider with two series resistors?+

Which model limit matters for Voltage divider with two series resistors?+

Retain Voltage divider with two series resistors for exams

Create a curated FSRS exam set for Uout = Uin·R₂/(R₁+R₂): formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.

Curated formula set · LaTeX · FSRS spaced repetition · import from Essential