# Wheatstone Bridge Circuit Theory and Working Principle

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Wheatstone bridge is used to measure unknown resistance and is defined by the circuit of the following figure.

In above Figure, R1, R2, and R3 are known resistances and Rx is the resistance whose value is to be determined. At least one of the known resistances is variable. The variable resistance is adjusted until no current flows through the galvanometer. When no current flows through the galvanometer, the circuit is in a null or balanced condition.

For the bridge to be balanced, point B and D must be at the same potential; for this to be true, the voltage from A to D must equal the voltage from A to B.

It follows that

${{I}_{1}}{{R}_{1}}={{I}_{3}}{{R}_{3}}$

Similarly,

${{I}_{2}}{{R}_{2}}={{I}_{X}}{{R}_{X}}$

Dividing one equation by the other, we obtain

$\frac{{{I}_{1}}{{R}_{1}}}{{{I}_{2}}{{R}_{2}}}=\frac{{{I}_{3}}{{R}_{3}}}{{{I}_{X}}{{R}_{X}}}~~~~~~~\cdots ~~~~~~~~\left( 1 \right)$

When no current in the galvanometer,

${{I}_{1}}={{I}_{2}}~~~~~~~~~~~~~~~~~and~~~~~~~~~~~~~~~~~~{{I}_{3}}={{I}_{X}}$

So eq. (1) reduces to

$\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{R}_{3}}}{{{R}_{X}}}$

Or

${{R}_{X}}=\frac{{{R}_{2}}}{{{R}_{1}}}*{{R}_{3}}$

Notice that bridge balance and the determination of Rx are completely independent of the magnitude of the source voltage. One must no use the bridge in an energized circuit. Also, lead resistance should be found and subtracted from subsequent resistance.

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