Question

If the wire is drawn out to three times its original length, by how much times would you expect its resistance to be increased

Answer 1

Let length be l
So new length is 3l
Since we didn't add any material to the wire while stretching it, its area of cross section changes from A to A/3
$r \alpha \frac{l}{a}$
So value of r is 9 times the earlier value.

Answer 2

Answer:

Hence the new resistance of the wire will be $9$ times.

Explanation:

The resistance of a wire is inversely proportional to its area and directly proportional to its length.

• When the length is tripled then resistance will also become three times.
• If the wire is stretched $3$ times the original length the cross section of the wire is cut to one third of its original cross section.
• The length while cutting the cross section by $3\times$ the new resistance will be nine ($9$) times the original resistance.
• As the formula goes $R=\frac{P}{A}$ (were p= resistivity of wire, l= length of wire and Ais cross section of wire)

Hence the new resistance of the wire will be $9$ times.