Question

The resistance of a wire of length L and area of cross-section a is $x$ ohm. If the wire is stretched to double its length, its resistance would become ______________.

• A. $2x$ ohm
• B. $0.5x$ oh
• C. $4x$ ohm
• D. $6x$ ohm

Answer 1

The correct option is C $4x$ ohm

$x=\frac{\rho L}{a}$

When the wire is stretched its area as well as length changes but volume remains constant

let new length be L'=2L and new area be a'

$L\times a=L^{\prime }\times a^{\prime }$

$\therefore a^{\prime }=\frac{a}{2}$

New resistance is equal to

$R=\frac{\rho L^{\prime }}{a^{\prime }}=\frac{\rho \times 2L}{a/2}=\frac{4\rho L}{a}=4x$