The source of e.m.f. and switch is connected to point A & B, while a sensitive current indicating meter the Galvanometer is connected to point C & D.

Galvanometer is a sensitive micro ammeter with a zero centre scale. When there is no current through the meter, the galvanometer pointer rests at 0,i.e. mid-scale. Current in one direction causes the pointer to deflect on one side and current in the opposite direction deflects it to the other side.

The resistor R1, R2 & R3 are known and Rx is unknown resistor to be measured.

When switch is closed, current flows and divides into the two arms at point A i.e. I1 & I2.

The bridge is balanced when there is no current through galvanometer or when the potential at points C & D are equal i.e. the potential across galvanometer is Zero. The When Bridge is balanced.

$\\\begin{gather*} I_1R_1\ =\ I_2R_2 \\ \\[2ex] I_1=I3=\dfrac{E}{R_1+R_3} \\ \\[2ex] I_2=I_4=\dfrac{E}{R_2+R_x} \\ \\[2ex] \dfrac{E\times R_1}{R_1+R_3}=\dfrac{E\times R_2}{R_2+R_x} \\ \\[2ex] \dfrac{R_1}{R_1+R_3}=\dfrac{R_2}{R_2+R_x} \\ \\[2ex] R_1R_2\ +\ R_1R_x\ =\ R_1R_2+R_2R_3 \\ \\[2ex] R_1R_x\ =\ R_2R_3 \\ \\[2ex] \ \ \ \ \ \ \ \ \ R_x=\ \dfrac{R_2R_3}{R_1} \\\end{gather*} $