Question

Derive the expression to find the unknown resistance in the balanced condition of Wheatstone bridge.

Answer 1

When there is no potential difference between points a and b there is no current flow between these points.

Hence all of current I1 flows through R1 and into R3, and all of current I2 flows through R2 and into Rx.

As there is no potential difference between points a and b, we also know that the potential difference across R1, must be equal to the potential difference across R2., i.e. that V1 = I1 R1 = I2 R2.

The potential differences across R3 and into Rx must also be equal, giving I1 R3 = I2 Rx.

We can now divide the second equation by the first to give R3 / R1= Rx/R2, and rearrange to obtain an expression for Rx. : Rx. = (R2 R3)/ R1.