Question

Two conductors A and B of have their lengths in ratio 4 : 3, area of cross-section in ratio 1 : 2 and their resistivities in ratio 2 : 3. What will be the ratio of their resistances?

Answer 1

The ratio of the resistances of the two conductors is 16:9

Explanation:

Given:

The ratio of lengths of two conductors

$\frac{l_1}{l_2}=\frac{4}{3}$

The ratio of cross-sectional areas of two conductors

$\frac{A_1}{A_2}=\frac{1}{2}$

The ratio of resistivities of two conductors

$\frac{\rho_1}{\rho_2}=\frac{2}{3}$

To find out:

The ratio of resistances $\frac{R_1}{R_2}$

Solution:

We know that

The relation between resistance $R$ length $l$, cross-sectional area $A$ and specific resistance $\rho$ of a conductor is given by

$\boxed{R=\rho\frac{l}{A}}$

Thus,

For two conductors

$R_1=\rho_1\frac{l_1}{A_1}$

And $R_2=\rho_2\frac{l_2}{A_2}$

$\frac{R_1}{R_2}=\frac{\rho_1}{\rho_2}\times\frac{l_1}{l_2}\frac{A_2}{A_1}$

$\implies \frac{R_1}{R_2}=\frac{2}{3}\times\frac{4}{3}\times\frac{2}{1}$

$\implies \frac{R_1}{R_2}=\frac{16}{9}$

$\implies R_1:R_2=16:9$

Hope this answer is helpful.

Know More:

Q: 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.

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