(N/A) Wheatstone bridge is a special arrangement of four resistors used to measure an unknown resistance. It consists of four resistors $R_{1}, R_{2}, R_{3}$,and $R_{4}$ arranged in a diamond shape,with a battery connected across two opposite junctions ($A$ and $C$) and a galvanometer connected across the other two junctions ($B$ and $D$).
The principle of the Wheatstone bridge is based on the condition of a balanced bridge. $A$ bridge is said to be balanced when no current flows through the galvanometer $(I_{g} = 0)$.
In the balanced condition,the potentials at points $B$ and $D$ are equal $(V_{B} = V_{D})$.
Applying Kirchhoff's laws for the balanced condition:
$1$. The potential drop across $R_{1}$ equals the potential drop across $R_{2}$,so $I_{1}R_{1} = I_{2}R_{2}$.
$2$. The potential drop across $R_{3}$ equals the potential drop across $R_{4}$,so $I_{3}R_{3} = I_{4}R_{4}$.
Since $I_{g} = 0$,we have $I_{1} = I_{3}$ and $I_{2} = I_{4}$.
Dividing the two equations gives the balancing condition: $\frac{R_{1}}{R_{3}} = \frac{R_{2}}{R_{4}}$ or $\frac{R_{1}}{R_{2}} = \frac{R_{3}}{R_{4}}$.