Calculation
Rx = RN · R₁ / R₂
At null balance the bridge midpoints have equal potential, giving Rx = RN·R₁/R₂.
Busch 2006, Gleichung zur Wheatstone-Abgleichbedingung
Balanced Wheatstone bridge
At null balance the bridge midpoints have equal potential, giving Rx = RN·R₁/R₂.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Unknown resistance Rx — Resistance in the measurement arm after the null detector shows zero bridge current.
- Reference resistance RN — Known, sufficiently accurate reference resistor in the opposite bridge arm.
- Ratio resistor R₁ — Known resistor on the same potential side as Rx; its ratio to R₂ sets the measurement factor.
- Ratio resistor R₂ — Known resistor in the second ratio arm; never enter zero.
Example
RN=100 Ω, R₁=150 Ω and R₂=100 Ω give Rx=150 Ω at null balance.
Assumptions and limits
Ideal DC null balance; lead, contact and self-heating errors and residual bridge voltage are excluded.
Understand Balanced Wheatstone bridge
This calculator determines an unknown resistance from a true Wheatstone-bridge null balance. It is useful for learning the balance condition and evaluating a laboratory setup.
What does this quantity describe?
At balance no current flows through the null detector because both bridge midpoints have equal potential. Rx then depends only on reference RN and ratio R₁/R₂, not on supply voltage or detector resistance.
Formula and variables
Rx = RN · R₁ / R₂
Rx = RN · R₁ / R₂Balance condition: UAB = 0
| Symbol / input | Meaning |
|---|---|
| Unknown resistance Rx | Resistance in the measurement arm after the null detector shows zero bridge current. |
| Reference resistance RN | Known, sufficiently accurate reference resistor in the opposite bridge arm. |
| Ratio resistor R₁ | Known resistor on the same potential side as Rx; its ratio to R₂ sets the measurement factor. |
| Ratio resistor R₂ | Known resistor in the second ratio arm; never enter zero. |
Choose the inputs correctly
RN is the known reference resistor. R₁ and R₂ are the ratio arms and their labels must match the actual circuit. Use calibrated values or the bridge-wire reading at the exact null position.
How to use the calculator
Energise the bridge, adjust R₁/R₂ until diagonal current is zero, then enter RN, R₁ and R₂. Rx is valid only for that balanced setting.
Worked example
RN=100 Ω, R₁=150 Ω and R₂=100 Ω give Rx=150 Ω.
Understand the result and units
Rx scales directly with RN and R₁ and inversely with R₂. Swapping the ratio arms therefore inverts the intended measurement factor.
All quantities are resistances; mixed Ω, kΩ and MΩ inputs are converted internally.
Typical applications
Resistance measurement labs, strain-gauge and temperature-sensor bridge balancing, and plausibility checks of classical null methods.
Assumptions, limits and common mistakes
Only a balanced DC bridge is evaluated. An unbalanced bridge needs an output-voltage model; AC bridges require complex impedances and phase balance.
Common mistake: Do not calculate while the detector still deflects. Trace the actual circuit labels for R₁ and R₂ instead of guessing from drawing position.
Frequently asked questions
What is “Balanced Wheatstone bridge” used for?
Resistance measurement labs, strain-gauge and temperature-sensor bridge balancing, and plausibility checks of classical null methods.
Where do the input values come from?
RN is the known reference resistor. R₁ and R₂ are the ratio arms and their labels must match the actual circuit. Use calibrated values or the bridge-wire reading at the exact null position.
What does the result not cover?
Only a balanced DC bridge is evaluated. An unbalanced bridge needs an output-voltage model; AC bridges require complex impedances and phase balance.