## Section36.6The Wheatstone Bridge

Perhaps the most famous bridge circuit is the Wheatstone bridge, which is used to measure resistances accurately.

The Wheatstone bridge circuit, shown in Figure 36.6.1, consists of four resistors connected to form a quadrilateral. One of the sides of the quadrilateral contains the unknown resistor $R_{\times}\text{,}$ another contains a variable resistor $R_V$ and the remaining two contain high precision resistors $R_1$ and $R_2\text{.}$ A voltage source V is connected to two opposite corners.

When there is no current in the AGB branch, then the circuit becomes simply a circuit of two resistances $R_1+R_{\times}$ and $R_2+R_V$ in parallel, and we can use the simple parallel circuits analysis to figure out the relation at the null condition.
At the null condition, let current $I_1$ flow through the upper branch containing $R_1$ and $R_\times\text{,}$ and $I_2$ flow through the lower branch containing $R_2$ and $R_V\text{.}$ At the null condition, the potential drop across $R_1$ will equal the potential drop across $R_1\text{.}$ Similarly, the potential drop across $R_\times$ will equal the potential drop across $R_V\text{.}$ Therefore, we will get