Wheatstone Bridge Calculator
Analyze bridge circuits and check for balance.
What is a Wheatstone Bridge?
A Wheatstone bridge represents a precise electrical circuit used to measure unknown electrical resistance with high accuracy. Invented by Samuel Hunter Christie and popularized by Sir Charles Wheatstone in 1843, this circuit remains the gold standard for measuring small resistance changes.
The circuit consists of two voltage dividers connected in parallel, with a galvanometer (or voltmeter) bridging the center nodes. When the bridge is "balanced," the voltage difference is zero, allowing for precise calculation of an unknown resistor.
How to Calculate Output Voltage (The Formula)
The bridge output voltage (Vg) is the difference between the potentials of the two legs.
Vg = Vin × [ (Rx / (R3 + Rx)) - (R2 / (R1 + R2)) ]
Balanced Condition
The bridge is considered balanced when Vg = 0. At this point, the ratio of resistances in the known arm equals the ratio in the unknown arm:
R1 / R2 = R3 / Rx OR Rx = (R2 / R1) × R3
Practical Applications
While originally used for manual resistance measurement, the Wheatstone bridge is now the heart of modern sensor technology:
- Strain Gauges: Measuring structural stress in bridges, aircraft wings, and machinery. As the gauge deforms, its resistance changes slightly, which the bridge converts to a measurable voltage.
- Load Cells: Digital scales use Wheatstone bridges to weigh objects.
- Thermistors and RTDs: Precise temperature measurement devices often use a bridge configuration to linearize the output and improve sensitivity.
FAQ
What is a balanced bridge?
A balanced bridge is a state where the output voltage difference between the two legs is exactly zero. This means the ratio of resistances on the left side matches the ratio on the right side. This null-point method is extremely accurate because it is independent of the source voltage fluctuations.
Why use a bridge instead of a simple voltage divider?
A simple voltage divider is sensitive to source noise and has non-zero offset. A Wheatstone bridge is a differential measurement, meaning it rejects common-mode noise and allows for measuring very small changes (like 0.1%) around a zero point, offering far superior sensitivity for sensors.
How does temperature affect the bridge?
If resistors change value with temperature, the bridge can drift. However, this property is often used to our advantage in "temperature compensation" schemes, where a dummy gauge is used in the adjacent arm to cancel out thermal effects.