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Wheatstone Bridge · Balance Condition and Sensitivity

Classic bridge circuit | Adjust the bridge-arm resistors to observe the galvanometer current | Balance condition \(R_1/R_2 = R_3/R_x\)
\(U_{in} = 10\text{V}\) (fixed) | Galvanometer internal resistance \(R_G = 100\,\Omega\)

Bridge Arm Resistance Settings

Resistance \(R_1\) (top left arm) 1000 Ω

10 Ω10 kΩ

Resistance \(R_2\) (top right arm) 1000 Ω

10 Ω10 kΩ

Resistance \(R_3\) (bottom left arm) 1000 Ω

10 Ω10 kΩ

Resistance \(R_x\) (bottom right arm, unknown) 1000 Ω

10 Ω10 kΩ

Input Voltage \(U_{in}\) 10.00 V

Fixed DC voltage source

Wheatstone Bridge Topology

Bridge Circuit Structure

\(U_a = U_{in}\frac{R_2}{R_1+R_2}\) \(U_b = U_{in}\frac{R_x}{R_3+R_x}\)
\(U_G = U_a - U_b\) \(I_G = U_G / R_G\)

Bridge Midpoint Voltages \(U_a\) and \(U_b\)

At balance, both bars are equal height

Blue = \(U_a\) (left voltage divider midpoint) | Orange = \(U_b\) (right voltage divider midpoint)

Galvanometer Indicator · Current \(I_G\)

Direction and magnitude

← Left

Right →

I_G = 0.000 μA (zero)

Bridge Arm Voltage and Galvanometer

\(U_a\) (upper midpoint a) — V

\(U_b\) (lower midpoint b) — V

\(U_G = U_a - U_b\) — V

\(I_G = U_G / R_G\) — μA

Balance Status

Not Balanced ✗

\(R_1 / R_2\) —

\(R_3 / R_x\) —

Wheatstone Bridge Balance Principle

When the bridge arm resistors satisfy \(R_1/R_2 = R_3/R_x\) (i.e., \(R_1 R_x = R_2 R_3\)), the galvanometer voltage \(U_G = 0\) and the bridge is balanced. At this point \(U_a = U_b\) and no current flows through the galvanometer. Adjust all four bridge-arm resistors independently to see how the circuit reaches, or departs from, balance. At balance, \(R_x = R_2 R_3 / R_1\), which can be used for precise measurement of an unknown resistance.

Sensitivity and Galvanometer

Galvanometer internal resistance \(R_G = 100\,\Omega\), used to detect small imbalance currents. Bridge sensitivity depends on the galvanometer's current detection capability and the bridge arm resistance values. When \(U_G\) is near zero, the galvanometer needle is centered; away from balance, the current direction indicates the relative magnitudes of \(U_a\) and \(U_b\). Click the "Auto Balance" button to automatically adjust \(R_x\) to the balance value.