# Deriving Wheatstone bridge equation

I have the following circuit:

Here I have obtained the equation of Ud = U * ((deltaR / R)/(4+2(deltaR/R))). But I'm stuck on the part on how to derive that formula.

Any help or guidance is appreciated. (mainly since my book don't have the answer to this question that is within it)

• I think you should split this question in two different questions. Someone may know the answer to only one of them.
– Falk
Jun 1, 2020 at 9:38
• You wrote "I have the following circuit", but no circuit diagram follows. I think you should add it to the question. Jun 1, 2020 at 11:53
• Rolled back because image was removed. Please be careful Jun 1, 2020 at 12:18
• I have rolled this back (again) because the change made by the OP made my answer incorrect. I have used V1 and V2 in my answer and this should be maintained in the question. Don't mess with it is my strong advice. And now it appears that @scott has had the same thought! Jun 1, 2020 at 12:47

$$V1 = \dfrac{U}{2} \space\space\space\text{and}\space\space\space V2 = U\cdot\dfrac{R+\Delta R}{R+R+\Delta R}$$
$$\text{therefore}\space\space V2-V1 = U\cdot\left(\dfrac{R+\Delta R}{2R +\Delta R} - \dfrac{1}{2}\right)\space\space = U_d$$
$$U_d = U\cdot\left(\dfrac{\Delta R}{4R + 2\Delta R}\right)$$