Question

the copper wires length of L and 2L have radii R and 2r respectively the ratio of their specific resistance is

Answer 1

The answer is

$\boxed{ \boxed{ \boxed{2:1}}}$

STEP-BY-STEP EXPLANATION :-

We have two wires made up of copper.

This means that the Resistivity of both the wires will be same as they are made up of same material.

Now,

Radius of wire 1 is R

So,

Area of cross section of wire 1 will be :-

$\boxed{\pi {r}^{2}}$

Now,

Radius of wire 2 is 2R

So,

Area of cross section of the two wires will be :-

$\boxed{\pi {(2r )}^{2}} \\ \\ = \boxed{ \sf{4\pi {r}^{2}}}$

Now,

Ratio of Area 1/ Area 2 is equal to 1/4

Also,

Length 1 = L

Length 2 = 2L

So,

Ratio of L1/L2 is equal to 1/2

Now ,

We know that :-

$\boxed{\boxed{r = \frac{\rho \times l}{a}}}$

Now

Ratio of their specific resistance will be as follows :-

$\frac{r1}{r2} = \frac{ \frac{\rho \times l1}{a1} }{ \frac{\rho \times l2}{a2} } \\ \\ \\ = \mathcal{\frac{l1}{l2} \times \frac{a2}{a1}} \\ \\ \\ = \frac{1}{2} \times 4 = \frac{2}{1}$

So,

The ratio is equal to :-

$\boxed{\boxed{ \boxed{2:1}}}$