Question

Two copper wires are of the same length, but one is thicker than the other. Which wire will have more resistance?

Answer 1

Hint: As we know that resistance of any wire directly depends on the length of the wire and inversely varies with area. By using this relation, we can determine which wire will have more or less resistance.\[R \propto \dfrac{l}{A}\].Here $l$ is the length of the wire and $A$ is the area of the wire.

Complete answer:
As we know that resistance is directly proportional to the length of wire and inversely proportional to the area of wire.
\[R \propto \dfrac{l}{A}\] ---(1)
Here l is the length of wire and A is the area of the wire.
It means if length increases then also resistance will increase and if length decreases then the resistance will also decrease.

If area of the wire increases then the resistance will decrease and if area decreases then the resistance will increase.Now, according to the question, lengths of the copper wires are the same but one is thicker than the other. So, according to equation (1), thinner wire will have the more resistance. As resistance varies inversely with area. More the area, lesser will be resistance.

Hence, the wire which is less thicker will have higher resistance than the more thicker one.

Note: If length and area of the wire doubles then the resistance of wire will remain unaffected. If we talk about the specific resistance then both wires will have the same specific resistivity as it depends on the nature of material.