A block has dimensions 1 cm, 2 cm and 3 cm | vedclass

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(A) The resistance $R$ of a conductor is given by $R = \rho \frac{l}{A}$,where $\rho$ is the resistivity,$l$ is the length,and $A$ is the cross-sectio

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$9: 1$

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(A) The resistance $R$ of a conductor is given by $R = ho \frac{l}{A}$,where $ho$ is the resistivity,$l$ is the length,and $A$ is the cross-sectional area.Since $R \propto \frac{l}{A}$,to maximize $R$,we need the maximum length $l$ and the minimum area $A$.For the given dimensions $1 \ cm, 2 \ cm, 3 \ cm$:Maximum resistance $R_{\max} = ho \frac{3 \ cm}{(1 \ cm 	imes 2 \ cm)} = ho \frac{3}{2} \ cm^{-1}$.To minimize $R$,we need the minimum length $l$ and the maximum area $A$.Minimum resistance $R_{\min} = ho \frac{1 \ cm}{(2 \ cm 	imes 3 \ cm)} = ho \frac{1}{6} \ cm^{-1}$.The ratio $\frac{R_{\max}}{R_{\min}} = \frac{ho 	imes 1.5}{ho 	imes (1/6)} = 1.5 	imes 6 = 9$.Thus,the ratio is $9: 1$.

$A$ block has dimensions $1 \ cm, 2 \ cm$ and $3 \ cm$. The ratio of the maximum resistance to the minimum resistance between any pair of opposite faces of the block is:

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