Question

A 10 ohm wire is stretched so that it's length becomes three times its original length the new resistance of the wire will we?

Answer 1

Resistance ‘R = 10 ohm’ is related to length ‘L’, area of cross-section ‘A’ and resistivity ‘ρ’ as,

R = ρL/A

When L is tripled ,

As we know that the volume of the wire remains same.

old volume = new volume

AL = A'L' ....(i) ( as volume = area x length )

L' = 3L

So, from (i)

A' = A/3

So the new resistance is ,

R' = ρL'/A'

or

R' = ρ(3L)/(A/3) = 9 (ρL/A)

=> R' = 9R

so, the new resistance increases nine fold.

Now,

R' = 9 x 10ohms

thus,

R' = 90 ohms