Question

Why should the area of the cross-section of the meter bridge wire be uniform?

Answer 1

Meter bridge:

1. It is used to calculate highly accurate resistances.
2. It works on the principle of Wheatstone Bridge.

Cross-sectional area:

1. Let $R$ and $S$ be resistances such that $R=\frac{\rho x}{A}$and $S=\frac{\rho \left(100-x\right)}{A}$, where $\rho$ is specific resistivity, $x$ is length for resistance $R$, $100-x$ is length for resistance $S$ and $A$ is area.
2. So, the resistance will be given by $\frac{R}{S}=\frac{{\displaystyle \frac{\rho x}{A}}}{{\displaystyle \frac{\rho \left(100-x\right)}{A}}}$.
3. The areas in the above equation will cancel each other out, and the equation will be reduced to $\frac{R}{S}=\frac{{\displaystyle x}}{{\displaystyle 100-x}}$. This equation would have not been obtained if the areas were not the same and would have led to different resistances per unit length for different lengths.
4. So, in order to maintain the same resistance per unit length of bridge wire over different lengths, the area should be the same.

Hence, the area of the cross-section of the meter bridge wire should be uniform.