Wheatstone Bridge
Calculate unknown resistance using the Wheatstone bridge formula Rx = (R2/R1) × R3, or compute output voltage of an unbalanced bridge. Free online electronics calculator with charts and breakdowns.
About This Calculator
The Wheatstone Bridge Calculator helps electronics engineers, students, and hobbyists analyze Wheatstone bridge circuits. You can calculate the unknown resistance in a balanced bridge or determine the output voltage in an unbalanced bridge configuration. The calculator provides instant results, interactive charts, and detailed component breakdowns.
The Wheatstone bridge is a fundamental circuit in electrical engineering, invented by Samuel Hunter Christie in 1833 and later popularized by Sir Charles Wheatstone. It works on the principle of null measurement — comparing an unknown resistance against three known resistances arranged in a diamond configuration. When balanced, the ratio R1/R2 equals R3/Rx, allowing precise calculation of the unknown resistance Rx = (R2/R1) × R3.
For unbalanced bridges, the output voltage VG is calculated using VG = Vin × (R1/(R1+R2) − R3/(R3+Rx)). This mode is essential for sensor applications where small resistance changes (such as in strain gauges or thermistors) produce measurable voltage changes.
Key applications include strain gauge measurement for structural health monitoring, temperature sensing with platinum resistance thermometers (PRTs), pressure sensors in industrial automation, and load cells for weighing systems. The Wheatstone bridge's ability to detect minute resistance changes makes it indispensable in precision instrumentation.
How to use
Select "Find Unknown Resistance" mode and enter R1, R2, R3 to calculate Rx for a balanced bridge. Or select "Output Voltage" mode and enter all four resistances plus supply voltage to compute VG. The chart visually compares the resistance values across all bridge arms.
Frequently Asked Questions
What is a Wheatstone bridge?
A Wheatstone bridge is an electrical circuit invented by Charles Wheatstone that measures unknown resistance by balancing two legs of a bridge circuit. It consists of four resistors arranged in a diamond shape with a galvanometer connected between the two midpoints. When the bridge is balanced (no current flows through the galvanometer), the ratio of resistances in one leg equals the ratio in the other: R1/R2 = R3/Rx.
How do you calculate unknown resistance using a Wheatstone bridge?
For a balanced Wheatstone bridge, the unknown resistance Rx is calculated using the formula Rx = (R2/R1) × R3. For example, if R1 = 6 Ω, R2 = 9 Ω, and R3 = 4 Ω, then Rx = (9/6) × 4 = 6 Ω. The bridge is balanced by adjusting the variable resistor until the galvanometer reads zero.
How do you calculate the output voltage of an unbalanced Wheatstone bridge?
For an unbalanced Wheatstone bridge, the output voltage VG across the galvanometer is calculated using the formula VG = Vin × (R1/(R1+R2) − R3/(R3+Rx)), where Vin is the supply voltage. When VG = 0, the bridge is balanced and no current flows through the galvanometer.
What is the Wheatstone bridge used for?
Wheatstone bridges are used for precise resistance measurement, strain gauge sensors (to detect mechanical deformation), temperature measurement with thermistors, pressure sensors, and load cells. The circuit is valued for its high accuracy since it detects zero current rather than measuring a voltage or current directly.
What is the balanced condition of a Wheatstone bridge?
A Wheatstone bridge is balanced when the potential difference between the two midpoints (B and D) is zero, meaning no current flows through the galvanometer. The balanced condition satisfies the equation R1/R2 = R3/Rx. At balance, the product of opposite arm resistances are equal: R1 × Rx = R2 × R3.
What are the four arms of a Wheatstone bridge?
The four arms of a Wheatstone bridge are labeled R1 (arm AD), R2 (arm DC), R3 (arm AB), and Rx (arm BC). R1 and R3 are typically fixed resistors, R2 is a variable resistor, and Rx is the unknown resistance being measured. The supply voltage is applied across terminals A and C, while the galvanometer connects between B and D.
How accurate is a Wheatstone bridge for measuring resistance?
A Wheatstone bridge can measure resistance with accuracy up to four significant figures. The precision comes from the null measurement method — instead of measuring current or voltage directly, the bridge detects when the current is exactly zero using a sensitive galvanometer. This makes it one of the most accurate methods for measuring medium-range resistances (1 Ω to 1 MΩ).
What is the difference between balanced and unbalanced Wheatstone bridge?
In a balanced Wheatstone bridge, the ratio R1/R2 equals R3/Rx, so no current flows through the galvanometer and the output voltage is zero. In an unbalanced bridge, the ratios are unequal, causing a non-zero output voltage proportional to the imbalance. Balanced bridges are used for measuring unknown resistance, while unbalanced bridges are used in sensor applications like strain gauges where resistance changes are detected as output voltage changes.