Question

The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then(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 1

Explanation:

The electric resistance of a wire is given by :

$R=\rho\dfrac{l}{A}$

$\rho$ is resistivity

l is length of wire

A is area of cross section

If both length and radius are both doubled, i.e. l' = 2l and A' = 2A. New resistance of the wire becomes,

$R'=\rho\dfrac{l'}{\pi r'^2}\\\\R'=\rho\dfrac{(2l)}{\pi (2r)^2}\\\\R'=\rho\dfrac{(2l)}{4\pi r^2}\\\\R'=\dfrac{1}{2}\times \rho\dfrac{l}{\pi r^2}\\\\R'=\dfrac{1}{2}\times R$

So, the new resistance reduced by halved.

The resistivity of a wire is its property. It remains the same under every condition.

Hence, the correct option is (c) "the resistance will be halved and the specific resistance will remain unchanged".

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Answer 2

Answer:

specific resistance ≅ Resistivity (f) depends on 

the material of the wire and as according 

to the question both wires are of same

material ⇒ resistivity of both wires is same.