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

\(-I_{2}R_{3}+0+I_{1}R_{1}=0\)

Considering the loop RQSR

\(I_{1}R_{2}+0-I_{2}R_{x}=0\)

From the first loop

\(\frac{I_{2}}{I_{1}}=\frac{R_{1}}{R_{3}}\)

From second loop

\(\frac{I_{2}}{I_{1}}=\frac{R_{2}}{R_{x}}\)

Hence to find the unknown resistance

\(\frac{R_{1}}{R_{3}}=\frac{R_{2}}{R_{x}}\) \(R_{x}=\frac{R_{2}R_{3}}{R_{1}}\)

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