Question

A steel wire of length L and radius r1 has a resistance R. A second steel wire has the same length but a radius r2 and a resistance of 2R. Find the ratio r1/r2.

Answer 1

answer should be 1/2^1/2 because resistance is inversly proportional to square of the radious of the cross section

Answer 2

Given that,

Two wires of same length L and radius $r_1\ and\ r_2$. R is the resistance of wire 1.

To find,

Ratio of resistance of first to second wire.

Solution,

The resistance of wire 1 is :

$R=\rho\dfrac{L}{A}\\\\R=\rho\dfrac{L}{\pi r_1^2}\ .......(1)$

2R is the resistance of second wire such that,

$2R=\rho\dfrac{L}{A}\\\\2R=\rho\dfrac{L}{\pi r_2^2}\ ........(2)$

Dividing equation (1) and (2) we get :

$\dfrac{R}{2R}=\dfrac{\dfrac{\rho L}{\pi r_1^2}}{\dfrac{\rho L}{\pi r_2^2}}\\\\\dfrac{1}{2}=\dfrac{r_2^2}{r_1^2}\\\\\dfrac{r_1}{r_2}=\sqrt{2}$

So, the ratio of radius of wire 1 to the wire 2 is $\sqrt{2} :1$.

Learn more,

Resistance

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