Question

A given wire of resistance $1\Omega$ is stretched to double its length. What will be its new resistance?

• A. $1\Omega$.
• B. $8\Omega$.
• C. $2\Omega$.
• D. $4\Omega$.

Answer 1

Answer: (D)

$4\Omega$.

When we stretch a wire to make its length double or whatever the size, to conserve volume, its cross-sectional area must decrease. For a common observation, when we stretch something its length increases but thickness decreases. Now the tricky part is in the question we are being told the new length but not the cross-sectional area, so we have to find it first.

Let's say a wire having length L cross-sectional area A has resistance R. If it is so stretched that its length becomes 2L so new length L' = 2L and when the length is doubled by stretching the cross-sectional area decreases by half.

The resistance of the wire is expressed as $R=\frac{\rho L}{A}$where,

rho is the resistivity of the wire,

L is the length of the wire,

A is the area of the cross-section of the wire.

The new resistance is calculated as follows.

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

That is, the new resistance is four times the old resistance.

Hence, the new resistance is $1\times 4=4ohms$.