Wheatstone bridge -- Why set all 4 resistances equal?

[arvindsharma]

Can someone explain me,why Wheatstone bridge is most sensitive when all four resistances say A,B,C and D are equal?as far as i know condition for Wheatstone Bridge is A/B=C/D.

 

[jim hardy]

Wheatstone bridges used to employ a galvanometer as a null detector.

Solve the bridge for current through the galvanometer ...

 

[zoki85]

Can someone explain me,why Wheatstone bridge is most sensitive when all four resistances say A,B,C and D are equal?as far as i know condition for Wheatstone Bridge is A/B=C/D.

Recipe:

From theoretical considerations of the bridge circuit, current through the ideal galvanometer can be understand as function of 4 variables:

I_AC=V⋅f(R₁,R₂,R₃,R₄)​

Definition of the sensitivity is:

S=dI_AC/dR_x​

where R_x can stand for any of R₁,R₂,R₃ or R₄.

Say R_x=R₄ and given the condition of the balance R₄=R₂⋅R₃/R₁, one searches for the stationary points of multivariable function S by solving the system:

∂S/∂R₁=0
∂S/∂R₂=0
∂S/∂R₃=0
...​

 

[Mike_In_Plano]

You can vary the thing and still get good results. i.e. the right leg has the same ratio as the left leg is good and sufficient.

To see why the system works better with equal values, find di / dRtest (i in galvenometer) as a function of the values with one value, Rtest set. Then set di/dR to zero to find the maximum sensitivity...