Question

The ratio of resistivities of two materials a and b is 1:2, ratio of their length is3:4 and if the ratio is 2:3 find the ratio of resistance of a and b

Answer 1

Assuming that the cross-sectional areas are not equal.

We know

R=ρlAR=ρlA

R=ρl2AlR=ρl2Al

R=ρl2VR=ρl2V

Where VV is the volume of each wire. Let dd be the density.

d=mV⟹V=mdd=mV⟹V=md

R=ρl2dmR=ρl2dm

Answer 2

Answer: The ratio of the resistance of a and b is 1:2.

Explanation:

Given that,

Ratio of resistivity of two materials

$\dfrac{\rho_{1}}{\rho_{2}} =\dfrac{1}{2}$

Ratio of their length

$\dfrac{l_{1}}{l_{2}}= \dfrac{3}{4}$

Ratio of the area

$\dfrac{A_{1}}{A_{2}}=\dfrac{2}{3}$

We know that,

The ratio of resistivity is

$\dfrac{R_{1}}{R_{2}}=\dfrac{\rho_{1} l_{1}}{A_{1}}\times \dfrac{A_{2}}{\rho_{2}l_{2}}$......(I)

Put the values of resistivity, length and area in equation (I)

$\dfrac{R_{1}}{R_{2}}=\dfrac{1\times 3\times 2}{2\times 2\times 3}$

$\dfrac{R_{1}}{R_{2}}= \dfrac{1}{2}$

Hence, The ratio of the resistance of a and b is 1:2.