Question

A wire of resistivity ? must be replaced in a circuit by a wire four times as long. If, however, the

Answer 1

Answer:

E) be two times larger.

Explanation:

As we know that the relation between the resistance and the resistivity of the wire is given as:

$R=\rho.\frac{l}{a}$

where:

$\rho=$ resistivity of the wire

$l=$ length of wire

$a=$ area of wire

$R=$ resistance

Now, when the length of the wire is four times the initial length then for the resistance to remain constant:

$R=\rho.\frac{4l}{a'}$

where:

$a'=$ area of the new wire

$\rho.\frac{l}{a} =\rho.\frac{4l}{a'}$

$a'=4a$

we know that area of the cross section of wire is given as:

$a=\pi.r^2$

$\pi.r'^2=4\times \pi.r^2$

$r'=2r$

Hence the radius must be twice of the initial radius for the resistance to be constant when length is taken four times.