Question

A rectangular metal block has dimensions $3cm\times 1cm\times 1cm$. The ratio of the resistance measured between the two opposite rectangular faces to that measured between the two square forces of the block is:

• A. $1:3$
• B. $1:9$
• C. $3:1$
• D. $9:1$

Answer 1

The correct option is B $1:9$

Resistance between the opposite rectangular faces is
$R_1=\frac{\rho l}{A}=\frac{\rho \times 1}{3}=\frac{\rho }{3}$
Resistance between the two opposite square faces is
$R_2=\frac{\rho l}{A}=\frac{\rho \times 3}{1}=3\rho$
$\Rightarrow \frac{R_1}{R_2}=\frac{\frac{\rho }{3}}{3\rho }=\frac{\rho }{3}\times \frac{1}{3\rho }=\frac{1}{9}$