Wheatstone Bridge Circuit diagram is as shown in the picture below
R3 = Adjustable Resistance
R1 and R2 are known Resistances
Rx = Unknown Resistance
G = Galvanometer connected between Q and S
Battery connected between P and R terminals
I(1)= current that passes through R1 and R2
I(2) = current that passes through R3 and Rx
Considering the loop PSQP
\(\begin{array}{l}-I_{2}R_{3}+0+I_{1}R_{1}=0\end{array} \)
Considering the loop RQSR
\(\begin{array}{l}I_{1}R_{2}+0-I_{2}R_{x}=0\end{array} \)
From the first loop
\(\begin{array}{l}\frac{I_{2}}{I_{1}}=\frac{R_{1}}{R_{3}}\end{array} \)
From second loop
\(\begin{array}{l}\frac{I_{2}}{I_{1}}=\frac{R_{2}}{R_{x}}\end{array} \)
Hence to find the unknown resistance
\(\begin{array}{l}\frac{R_{1}}{R_{3}}=\frac{R_{2}}{R_{x}}\end{array} \)
\(\begin{array}{l}R_{x}=\frac{R_{2}R_{3}}{R_{1}}\end{array} \)
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