Engineering · Electrical engineering/Control

Balance condition of a Wheatstone bridge

At bridge balance, the voltage between the middle nodes is zero and the resistance ratios match.

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Formula

\frac{R _{1}}{R _{2}} = \frac{R _{3}}{R _{4}}

R in Ω; ratio dimensionless

Variables & units

Variables & units
Symbol	Meaning	Unit
R1–R4	Four bridge resistors in the stated arrangement	Ω

LaTeX

\frac{R_1}{R_2}=\frac{R_3}{R_4}

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Derivation & background

The condition follows from equal divider ratios in the two bridge branches; ideally no current flows through the detector. Resistor placement depends on the circuit drawing. Lead resistance, detector loading and temperature drift shift a practical null balance.

Exam blueprint

Validity range

Derivation steps

At bridge balance, the voltage between the middle nodes is zero and the resistance ratios match.

1State the model assumptions and list quantities with units.
2Substitute into R₁/R₂ = R₃/R₄; convert quantities to SI first.
3With R1=100 Ω, R2=200 Ω and R3=150 Ω, balance requires R4=300 Ω.

Rearrangements

Base equation for the target quantity

\frac{R_1}{R_2}=\frac{R_3}{R_4}

Preserve signs, boundary conditions and units when rearranging.

Task variant

Work through the numerical example for “Balance condition of a Wheatstone bridge” and check its unit and magnitude.

With R1=100 Ω, R2=200 Ω and R3=150 Ω, balance requires R4=300 Ω.

Common mistakes

Substituting a related quantity that shares the same symbol.

Use variable definitions and check: R in Ω; ratio dimensionless.

Exam context

Measure an unknown resistance with a null-balance bridge.

Formula cluster

Electrical engineering/Control

At bridge balance, the voltage between the middle nodes is zero and the resistance ratios match.

UTh = Uoc; RTh = Uoc/Isc

Thevenin equivalent of a linear two-terminal network

Uout = Uin·R₂/(R₁+R₂)

Voltage divider with two series resistors

U = R·I

Ohm's Law

Worked example

With R1=100 Ω, R2=200 Ω and R3=150 Ω, balance requires R4=300 Ω.

Applications

Measure an unknown resistance with a null-balance bridge.

How do you calculate with Balance condition of a Wheatstone bridge?

Here is how to work through a typical Balance condition of a Wheatstone bridge (R₁/R₂ = R₃/R₄) task step by step:

1
Task
Work through the numerical example for “Balance condition of a Wheatstone bridge” and check its unit and magnitude.
Solution path
With R1=100 Ω, R2=200 Ω and R3=150 Ω, balance requires R4=300 Ω.

Frequently asked questions about Balance condition of a Wheatstone bridge

When is bridge voltage zero?+

The midpoint potentials match when both dividers have the same ratio. Then no ideal current flows through the detector. The displayed resistor assignment is convention-dependent; swapping positions changes the ratio expression. Resistor numbering must match the actual bridge diagram and detector terminals. Application: Measure an unknown resistance with a null-balance bridge. The numerical example With R1=100 Ω, R2=200 Ω and R3=150 Ω, balance requires R4=300 Ω anchors the idea in a concrete measurement case. The corresponding units are R in Ω; ratio dimensionless. With R1=100 Ω, R2=200 Ω and R3=150 Ω, balance requires R4=300 Ω. This checks that the reference quantities are compatible.

How can an unknown resistance be found?+

Adjust an arm or use known reference resistors until the detector reads zero. Solve the ratio for the unknown. Null balance reduces dependence on detector calibration, but leads and contact resistance remain error sources. Resistor numbering must match the actual bridge diagram and detector terminals. The corresponding units are R in Ω; ratio dimensionless. With R1=100 Ω, R2=200 Ω and R3=150 Ω, balance requires R4=300 Ω. This checks that the reference quantities are compatible. Scope: The condition follows from equal divider ratios in the two bridge branches; ideally no current flows through the detector. Resistor placement depends on the circuit drawing. Lead resistance, detector loading and temperature drift shift a practical null balance. A practical application is Measure an unknown resistance with a null-balance bridge.

Why can null balance be precise?+

At balance, the instrument need not quantify a small voltage; it mainly detects the null. Accuracy is then limited by reference resistors, contact stability and thermal drift. Four-wire methods are often needed for very low resistances. Resistor numbering must match the actual bridge diagram and detector terminals. Scope: The condition follows from equal divider ratios in the two bridge branches; ideally no current flows through the detector. Resistor placement depends on the circuit drawing. Lead resistance, detector loading and temperature drift shift a practical null balance. A practical application is Measure an unknown resistance with a null-balance bridge.

How do I check the result and units for Balance condition of a Wheatstone bridge?+

Write the quantity and unit from the variable list next to every value: R in Ω; ratio dimensionless. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example With R1=100 Ω, R2=200 Ω and R3=150 Ω, balance requires R4=300 Ω. 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. Resistor numbering must match the actual bridge diagram and detector terminals.

Which model limit matters for Balance condition of a Wheatstone bridge?+

The background states this starting condition: The condition follows from equal divider ratios in the two bridge branches; ideally no current flows through the. 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. Resistor numbering must match the actual bridge diagram and detector terminals.

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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]MIT OpenCourseWare, Circuits and Electronics, bridge circuits and resistor networks.

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\sum I_{\mathrm{in}}=\sum I_{\mathrm{out}}, \qquad \sum_{\mathrm{Masche}}\Delta V=0

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Ideal PID controller transfer function

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

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

Current rise in an RL circuit

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Create a curated FSRS exam set for R₁/R₂ = R₃/R₄: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.

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Symbol

Meaning

Unit

R1–R4

Four bridge resistors in the stated arrangement

Exam blueprint

Validity range

Derivation steps

At bridge balance, the voltage between the middle nodes is zero and the resistance ratios match.

1State the model assumptions and list quantities with units.
2Substitute into R₁/R₂ = R₃/R₄; convert quantities to SI first.
3With R1=100 Ω, R2=200 Ω and R3=150 Ω, balance requires R4=300 Ω.

How do you calculate with Balance condition of a Wheatstone bridge?

Here is how to work through a typical Balance condition of a Wheatstone bridge (R₁/R₂ = R₃/R₄) task step by step:

Task

Work through the numerical example for “Balance condition of a Wheatstone bridge” and check its unit and magnitude.

Solution path

With R1=100 Ω, R2=200 Ω and R3=150 Ω, balance requires R4=300 Ω.

Frequently asked questions about Balance condition of a Wheatstone bridge

When is bridge voltage zero?+

How can an unknown resistance be found?+

Why can null balance be precise?+

How do I check the result and units for Balance condition of a Wheatstone bridge?+

Which model limit matters for Balance condition of a Wheatstone bridge?+

Retain Balance condition of a Wheatstone bridge for exams

Create a curated FSRS exam set for R₁/R₂ = R₃/R₄: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.

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