Question

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

Answer 1

Answer:

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

Answer 2

Answer:

Explanation:

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