Use the resistance formula

For a wire, $R = \rho \frac{L}{A}$ where:

• $\rho$ = resistivity
• $L$ = length
• $A$ = cross-sectional area

Wire is stretched to double its length

New length: $L' = 2L$

When a wire is stretched, its volume remains constant: $AL = A'L'$

So, $A' = \frac{AL}{L'} = \frac{AL}{2L} = \frac{A}{2}$

Find the new resistance

$R' = \rho \frac{L'}{A'} = \rho \frac{2L}{A/2} = \rho \frac{4L}{A} = 4R$

Calculate percentage increase

Increase in resistance: $\Delta R = R' - R = 4R - R = 3R$

Percentage increase: $\frac{\Delta R}{R} \times 100 = \frac{3R}{R} \times 100 = 300\%$

Final answer

$\boxed{300}$