Editing Wheatstone bridge (section)

== Operation ==
In the figure, {{math|''R<sub>x</sub>''}} is the fixed, yet unknown, resistance to be measured.
{{math|''R''<sub>1</sub>}}, {{math|''R''<sub>2</sub>}}, and {{math|''R''<sub>3</sub>}} are resistors of known resistance and the resistance of {{math|''R''<sub>2</sub>}} is adjustable. The resistance {{math|''R''<sub>2</sub>}} is adjusted until the bridge is "balanced" and no current flows through the  [[galvanometer]] {{math|''V<sub>g</sub>''}}. At this point, the [[potential difference]] between the two midpoints (B and D) will be zero.  Therefore the ratio of the two resistances in the known leg {{math|(''R''<sub>2</sub>&thinsp;/&thinsp;''R''<sub>1</sub>)}} is equal to the ratio of the two resistances in the unknown leg {{math|(''R<sub>x</sub>''&thinsp;/&thinsp;''R''<sub>3</sub>)}}.  If the bridge is unbalanced, the direction of the current indicates whether {{math|''R''<sub>2</sub>}} is too high or too low.

At the point of balance,
: <math>\begin{align}
  \frac{R_2}{R_1} &= \frac{R_x}{R_3} \\[4pt]
  \Rightarrow R_x &= \frac{R_2}{R_1} \cdot R_3
\end{align}</math>

Detecting zero current with a [[galvanometer]] can be done to extremely high precision. Therefore, if {{math|''R''<sub>1</sub>}}, {{math|''R''<sub>2</sub>}}, and {{math|''R''<sub>3</sub>}} are known to high precision, then {{math|''R<sub>x</sub>''}} can be measured to high precision. Very small changes in {{math|''R<sub>x</sub>''}} disrupt the balance and are readily detected.

Alternatively, if {{math|''R''<sub>1</sub>}}, {{math|''R''<sub>2</sub>}}, and {{math|''R''<sub>3</sub>}} are known, but {{math|''R''<sub>2</sub>}} is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of {{math|''R<sub>x</sub>''}}, using [[Kirchhoff's circuit laws]]. This setup is frequently used in [[strain gauge]] and [[resistance thermometer]] measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.