Question

the ratio of resistivity of two materials a and b is 1:2, ratio of their length is 3:4 and if the ratio of radii is 2:3 find the ratio of resistance of a and b.

Answer 1

The Resistance of a and b are in the ratio 27:32.
See descriptive answer in the pic

Answer 2

Answer:

The ratio of resistance of a and b is 27:32.

Explanation:

Given that,

The ratio of resistivity of two materials a and b is 1:2.

The ratio of their length is 3:4 and if the ratio of radii is 2:3.

The resistance of the wire is defined as,

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

Where, $\rho$ = resistivity of the materials

l = length  

A = area of cross section

We know that,

Area $A =\pi r^2$

The ratio of the resistance of a and b

$\dfrac{R_{a}}{R_{b}}=\dfrac{\dfrac{\rho_{a}l_{a}}{\pi r^2_{a}}}{\dfrac{\rho_{b}l_{b}}{\pi r^2_{b}}}$  

$\dfrac{R_{a}}{R_{b}}=\dfrac{\rho_{a}}{\rho_{b}}\times\dfrac{\pi r^{2}_{b}}{\pi r^{2}_{a}}\times\dfrac{l_{a}}{l_{b}}$....(I)

Put the value in the equation (I)

$\dfrac{R_{a}}{R_{b}}=\dfrac{1}{2}\times\dfrac{9}{4}\times\dfrac{3}{4}$

$\dfrac{R_{a}}{R_{b}}=\dfrac{27}{32}$

Hence, The ratio of resistance of a and b is 27:32.