Question

Two wires of a resistance wire having equal length differ in their thickness. One is thicker than the other. Which one of the two has higher resistance?

Answer 1

Concept used: Resistance of a wire

Step 1: Formula of resistance of a wire

The relation of resistance of a wire is given as:

$$\begin{gathered} R=\rho \frac{L}{A} \\ R=\rho \frac{L}{\pi r^2} \end{gathered}$$

Here, $\rho$ is the resistivity, L is the length of the wire, r is the radius of the wire and A is the area.

Step 2: Relation between resistance and thickness of wire

In the above formula, it is observed that resistance is inversely related to the area of the wire. So, if the area will increase, then the resistance will reduce. The wire of higher thickness will have a large area and less resistance.

Thus, the wire with less thickness will have higher resistance.