Wheatstone Bridge Formula

Wheatstone Bridge Circuit diagram is as shown in the picture below

R3 = Adjustable Resistance
Wheatstone Bridge Circuit diagram

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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