A wire has a resistance R. Find new resistance,
(i) if radius of cross-section of a cylindrical wire is doubled, then find ratio of initial to final resistance.
(ii) if length of wire is increased by `10%`, then find the percentage increase in its resistance.
(iii) if length of wire is increased by `20%`, then find the percentage increase in its resistance.

Options

A. 0.1
B. 0.2
C. 0.4
D. 0.21

Answer

D

Explanation

`l_(2)=1.1 l_(1),R_(2)-R_(1)=?`
`(R_(2))/(R_(1))=((l_(2))/(l_(1)))^(2)`
`R_(2)=((1.1 l_(1))/(l_(1)))^(2)xxR_(1)=1.21R_(1)`
Now increase in resistance `=R_(2)-R_(1)` and
% increase in resistance `=((R_(2)-R_(1))/(R_(1)))xx100`
`=((1.21R_(1)-R_(1))/(R_(1)))xx100`
`=21%`