A wire of length L and cross-sectional area A has resistance R.

What will be the resistance Rstretched of the wire if it is stretched to twice its original length? Assume that the density and resistivity of the material do not change when the wire is stretched.

Given:

L2 = 2 * L1

Using the formula,

Resistivity, d = (R * A) / L

Where,

R = resistance

A = area

L = length

1. d1 = (R1 * A1) / L1

2. d2 = (R2 * A2) / L2

Equating both 1 and 2 together,

(R2 * A2) / L2 = (R1 * A1) / L1

(R2 * A2) / (2 * L1) = (R1 * A1) / L1

Assume A1 = A2,

R2 = [ (R1 * A1) * 2 * L1] / (A1 * L1)

R2 = 2 * R1

The resistance will be twice the original resistance

Explanation:

This is a fairly simple question, the formular for the resistance of a wire is given as

R = rho * length / area

Where R = resistance

Rho = resistivity

L = length

A = area

Since the density and area are constant I. e they do not change

R / length = rho / area

The initial length is given as L, when this length is stretched to twice its original length, it becomes 2*L = 2L

Let x represent the resistance when the length is doubled

R / L = x / 2L

x = 2LR / L; dividing by L

We have that x = 2R; twice the resistance