Question

A wire of resistence 10ohm is drawn out so that its length is thriceits original length. Calculate its new resistence.

Answer 1

We have, initial resistance, R = 10 Ω

Original length be L and area of cross-section be A and the resistivity be ρ.

When the length is stretched to make it thrice, i.e. L/ = 3L, the area of cross-section A/ is such that,

AL = A/L/ [volume of the wire remains constant]

=> AL = A/(3L)

=> A/ = A/3

Now, the new resistance is,

R/ = ρL//A/ = ρ(3L)/(A/3)

=> R/ = 9ρL/A = (9)(10) = 90 Ω