Question

A metallic wire is doubled on itself. How do its specific resistance change?​

Answer 1

• When a given metallic wire is doubled on itself, its length is reduced to half, but its area of cross-section gets doubled. So, the resistance of the wire will become one-fourth i.e., the new resistance of wire will be R/4 (or 0.25 R).

Answer 2

Given,

A metallic wire is double on itself by length.

To find,

How does its specific resistance change when doubled?

Solution,

We know,

Resistance is directly proportional to the length.

= R ∝ L

And resistance is inversely proportional to the area of cross-section.

= R ∝ 1/A

= R ∝ L/A

Now, when the metallic wire is doubled, the length becomes half and the area of cross-section becomes doubled.

= R ∝ L/2 and R ∝ 1/ 2A

= R ∝ L/ 4A

= R ∝ R/4

Hence, the specific resistance is decreased by 1/4th of the original resistance.