Question

How does the resistance of a wire depend on its radius?

Answer 1

Explanation:

1. We know that the resistance of a wire is inversely proportional to the cross-sectional area of the wire.
2. However, the cross-sectional area of the wire is proportional to the square of the radius of the wire.
3. This means that the resistance of the wire and radius of the wire is inversely proportional to each other.
4. Therefore, as the radius increases, the resistance of the wire decreases. So, the resistance of a wire depends on its radius.
5. Formula:

$R\propto \frac{1}{A}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}or \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}R\propto \frac{1}{\pi r^2}$,

$R$ stands for the resistance of the conductor, $A$ is the cross-sectional area of ​​the conductor and $r$ is the radius of the wire.

This means if a wire of the same length, but of the double radius is taken, its resistance is found to be one-fourth.