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## Homework Statement

Consider the Wheatstone bridge as shown in the following figure, where ##e_0## is the Galvanometer reading. The condition for ##e_0 = 0 ## is called the null condition of the bridge. Using the Kirchhoff's rules, we can show that the condition is ## R_1R_4 = R_2 R_3##. Now I am trying to prove that if we interchange the emf and the galvanometer at the null position, then the current through the galvanometer is zero.

## Homework Equations

Kirchhoff's rules

## The Attempt at a Solution

Let ##I_i## be the current through the resistance ##R_i##. Now using the Kirchhoff's rules, we can write the following equations.$$I_1 R_1 + I_3 R_3 = I_2 R_2 + I_4 R_4$$

Now I have to exploit the null condition, ## R_1R_4 = R_2 R_3## to prove that the top and bottom point is at the same potential. Then the current through the galvanometer would be zero. But after lot of algebra I am unable to do that. Can anybody guide here ?

thanks