Question

two cubes A and B are of the same material the side of B is the thrice as that of A . find the ratio Ra/Rb

Answer 1

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Answer 2

Given :

Two cubes A and B are of the same material the side of B is the thrice as that of A .

Therefore , $L_b=3L_a$ .

To Find :

The ratio Ra/Rb .

Solution :

We know , resistance is given by :

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

So , $R_a=\dfrac{\rho L_a}{(L_a)^2}$

Therefore , $R_b=\dfrac{\rho L_b}{(L_b)^2}$

Putting , $L_b=3L_a$ , we get :

$R_b=\dfrac{3\rho L_a}{9L_a^2}\\\\R_b=\dfrac{1}{3}\dfrac{\rho L_a}{L_a^2}\\\\R_b=\dfrac{R_a}{3}$

Therefore , $\dfrac{R_a}{R_b}=3$ .

Learn More :

Resistance

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