Question

Does the resistance of a copper wire increase or decrease when both the length and diameter of the wire is doubled? Explain your reasoning.

Answer 1

Resistance will decrease as:

1. Length and diameter have doubled as resistance can be given as $R=\frac{\rho \mathcal{l}}{A}$ as Area is $A=\pi r^2$ here $r$ is radius so Diameter is doubled means radius is also doubled so the area will become 4 times now,
2. After putting new values of Area and Length, the new resistance will be half of the previous resistance.
3. So, the Resistance will decrease.