## The Wheatstone Bridge Calculator tool

The Wheatstone Bridge (also known as a single arm bridge) is one kind of instrument that can accurately measure Resistance. Figure 3-13 shows one of The common Wheatstone Bridges. Resistance R1, R2, R3, R4 are called the four arms of the bridge, and G is the galvanometer to check whether the branch it is in is current. When no current passes through G, the bridge is said to be in balance. At equilibrium, the Resistance values of the four arms satisfy one simple relation, which can be used to measure resistance.

Bridge voltage Calculator method 如下：

V_{B}= V_{in}*[Rx/(R3+Rx)- R2/(R1+R2)]

R3=R1, and Rx= R2+delta, Then

V_{B}= V_{in}*[
(R2+delta)/(R1+R2+delta)-R2/(R1+R2)]

Now, We assume that delta is greater than R1 + R2's is small, then

V_{B}= ~
V_{in}*[delta/(R1+R2)]

Therefore, We can see that the bridge voltage is approximately proportional to the error delta, divided by the sum of Resistance by one side.

Because of the bridge voltage, We can Calculator one unknown Resistance value.

(R1+R2)*(R3+Rx)*V_{B}/V_{in}= Rx*(R1+R2)+ R2*(R3+Rx)

Rx*(R1+R2)*V_{B}/ V_{in} + R3* (R1+R2)V_{B}/V_{in}= Rx*R1+Rx*R2 - R2*R3-
Rx*R2

Rx*R1 - Rx*(R1+R2)*V_{B}/ V_{in} = R2*R3 + R3*
(R1+R2)V_{B}/V_{in}

Rx = (R2*R3 + R3* (R1+R2)V_{B}/V_{in} )/ (R1- (R1+R2)*V_{B}/ V_{in})