The electric resistance of a certain wire of iron is R . If its length and radius are both doubled, then

Options

A. the resistance and the specific resistance, will both remain unchanged
B. the resistance will be doubled and the specific resistance will be halved
C. the resistance will be halved and the specific resistance will remain unchanged
D. the resistance will be halved and the specific resistance will be doubled

Answer

C

Explanation

`R= ( rho l_(1))/(A_(1))`, now `l_(2) = 2l_(1)`
`A_(2) = pi (r_(2) )^(2) = pi (2r_(1))^(2) = 4 pi r_(1)^(2) = 4 A_(1)`
`therefore R_(2) = (rho (2 l_(1)))/(4 A_(1)) = (rho l_(1))/( 2 A_(1))= (R)/(2)`
`therefore` Resistance is halved, but specific resistance remains the same.