Question

2. A uniform wire of resistance R is stretched until its length doubles. Assuming its density and resistivity remain constant, what is its new resistance

Answer 1

Answer:

Resistance is quadrupled.

Explanation:

Solving this requires us to use the formula of resistivity.

Resistivity is usually said to be the measure of the resistance of a particular size of any given material to the electrical conduction. It is mathematically represented as

ρ = RA/L, where

ρ = the resistivity of the given material

R = the resistance of the material

A = the area of the material

L = length of the material.

From the question, we're told that the length is doubled with the resistivity and density remaining constant. If the density is constant, this makes the volume constant as well.

Volume, V = A * L. We're then told that the length is doubled. If the length is doubled, for the volume to remain constant, then the area must be halved.

Volume, V = A/2 * 2L

Making, Resistance R, subject of the formula, we have

R = ρL/A.

Since resistivity is constant and the area is halved, we then have

R = 2L / (1/2A)

R = 4L / A

If the length is doubled, we have the resistance to be quadrupled