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

[latex]-I_{2}R_{3}+0+I_{1}R_{1}=0[/latex]

 

Considering the loop RQSR

[latex]I_{1}R_{2}+0-I_{2}R_{x}=0[/latex]

 

From the first loop

[latex]\frac{I_{2}}{I_{1}}=\frac{R_{1}}{R_{3}}[/latex]

 

From second loop

[latex]\frac{I_{2}}{I_{1}}=\frac{R_{2}}{R_{x}}[/latex]

 

Hence to find the unknown resistance

[latex]\frac{R_{1}}{R_{3}}=\frac{R_{2}}{R_{x}}[/latex]

 

[latex]R_{x}=\frac{R_{2}R_{3}}{R_{1}}[/latex]

 

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