🧮 Wheatstone Bridge Calculator

The Wheatstone Bridge, invented by Samuel Hunter Christie in 1833 and popularized by Sir Charles Wheatstone in 1843, is a circuit configuration used to measure an unknown electrical resistance with extraordinary precision. It consists of four resistors arranged in a diamond pattern with a voltage source connected across one diagonal and a galvanometer (sensitive current detector) across the other. When the bridge is "balanced," no current flows through the galvanometer, and the unknown resistance can be computed from the other three known values.

At balance, the ratio of resistances satisfies R₁ / R₂ = R₃ / R_x, so the unknown resistance is R_x = R₂ × R₃ / R₁. This null-type measurement is extremely accurate because it depends on resistance ratios rather than absolute voltage or current readings, eliminating errors from source voltage fluctuations and galvanometer calibration.

When the bridge is balanced, the voltage at the junction of R₁-R₃ equals the voltage at the junction of R₂-R_x, so zero current flows through the galvanometer. This happens when R₁/R₂ = R₃/R_x, or equivalently R₁ × R_x = R₂ × R₃.

The bridge is also used in sensor applications: strain gauges, thermistors, and pressure sensors replace one or more resistors. As the sensor resistance changes with temperature, pressure, or strain, the bridge goes slightly out of balance, producing a measurable voltage across the galvanometer terminals. This is the operating principle of most load cells and electronic scales.

1. Enter R₁, R₂, and R₃ values in ohms.
2. Leave Rₓ (the unknown) blank.
3. Click Calculate to solve for Rₓ.
4. Verify that R₁ × Rₓ ≈ R₂ × R₃ (balance check).
5. If solving for any other resistor, just leave that one blank instead.

What is the balance condition of a Wheatstone Bridge?

The bridge is balanced when R₁ × R_x = R₂ × R₃, meaning the products of opposite arms are equal. At balance, zero current flows through the galvanometer, and the unknown resistor can be found from the three known ones: R_x = R₂ × R₃ / R₁.

Why is the Wheatstone Bridge more accurate than a simple ohmmeter?

The bridge uses a null measurement: it detects zero current rather than measuring a voltage or current directly. This eliminates errors from source voltage fluctuations, meter calibration, and lead resistance. Accuracies of 0.01% or better are achievable.

What is the purpose of the galvanometer?

The galvanometer is a very sensitive current detector placed across the bridge. When the bridge is unbalanced, current flows through it in one direction or the other. At balance, the galvanometer reads exactly zero, confirming the resistance ratio is satisfied.

How are strain gauges related to the Wheatstone Bridge?

A strain gauge is a resistor whose value changes slightly when it is stretched or compressed. By placing it as one arm of a Wheatstone Bridge, tiny resistance changes (often less than 0.1%) produce a measurable output voltage. Most digital scales and load cells use this principle.

What happens if the bridge is slightly unbalanced?

A small voltage appears across the galvanometer terminals, proportional to the resistance imbalance. This output voltage can be amplified and measured. The relationship is approximately V_out = V_source × (ΔR / 4R) for small imbalances in a quarter-bridge configuration.

Can I use the Wheatstone Bridge for AC signals?

Yes, but with impedance instead of resistance. The AC bridge (or Maxwell Bridge, Wien Bridge) uses capacitors and inductors along with resistors. The balance condition then requires matching both magnitude and phase of the impedances, making AC bridges more complex to balance.

In practice, R₁ and R₂ are ratio arms (typically 10:1, 100:1, or 1:1), and R₃ is a precision decade resistance box that you adjust until the galvanometer reads zero. The sensitivity of the bridge depends on the source voltage: higher voltage means more sensitivity but also more self-heating of the resistors, which can shift their values. For measuring very low resistances (below 1 Ω), use a Kelvin Bridge (Kelvin Double Bridge), which eliminates lead and contact resistance errors. For very high resistances (above 1 MΩ), leakage currents across insulators become significant—use guarded measurements. The bridge is most accurate when all four resistors are of similar magnitude.