A copper wire of resistance `R_(0)` is strerched till its length is increased to n times of its original length. What will be its new resistance?

Options

A. 2R
B. 4R
C. 8R
D. 16R

Answer

B

Explanation

Resistance R of a wire of length l and cross-section area A with specific resistance `rho` for its material is given by
`R=(rhol)/(A)`
On stretching the volume remains constant `therefore Al=A.l.`
or `A.=(Al)/((2l))=(A)/(2)`
Let the resistance of the stretched wire be R..
`therefore R.=(rhol.)/(A.)=(rho(2l))/((A//2))=(4rhol)/(A)=4R`