Question

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

• A. $9:1$
• B. $1:9$
• C. $18:1$
• D. $1:6$

Answer 1

The correct option is A $9:1$

Given that,

The dimension of the block is 1cm, 3cm and 3cm.

The relation of the resistance of a conductor is

$R=\rho \frac{l}{A}....\left(I\right)$

Where,

$\rho$ = resistivity of the material of the conductor

$A$= area of the cross section of the conductor

$l$= length of the conductor

Now, the resistance is maximum

$R_{max}=\rho \times \frac{3}{1\times 2}$

$R_{max}=\frac{3\rho }{2}...\left(II\right)$

Now, the resistance is minimum

$R_{min}=\rho \frac{1}{2\times 3}$

$R_{min}=\frac{\rho }{6}...\left(III\right)$

Now, from equation (II) and (III)

The ratio of maximum resistance and minimum resistance is

$\frac{R_{max}}{R_{min}}=\frac{\frac{3\rho }{2}}{\frac{\rho }{6}}$

$\frac{R_{max}}{R_{min}}=\frac{3}{2}\times \frac{6}{1}$

$\frac{R_{max}}{R_{min}}=\frac{9}{1}$

$R_{max}:R_{min}=9:1$

Hence, the ratio is $9:1$