Question

The resistance, R, to electricity of a cylindrical-shaped wire is given by the equation R=pL/(pi)d^2 where p represents the resistivity of the wire’s material, L represents the length of the wire, and d represents the diameter of the wire.

What happens to the resistance of the wire as the diameter approaches 0?
The resistance approaches 0.
The resistance approaches pi.
The resistance approaches L.
The resistance approaches infinity.

Answer 1

The resistance approaches infinity

Explanation:

We are given

The resistance, R, to electricity of a cylindrical-shaped wire is given by the equation

`R=(\rho L)/(\pi (d)^2)`

where

p represents the resistivity of the wire’s material

L represents the length of the wire

d represents the diameter of the wire

now,

d approaches to 0

so, we can plug d=0 and find R

`R=(\rho L)/(\pi (0)^2)`

`R=(\rho L)/(0)`

`R=\infty`

So,

The resistance approaches infinity