Question

The sides of rectangular block are $2m,3m$ and $4m$. The ratio of the maximum to minimum resistance between it's parallel faces is.

• A. $4:1$
• B. $3:2$
• C. $2:1$
• D. $1:3$

Answer 1

The correct option is A $4:1$

Resistance of the wire is,

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

where $\rho =$ resistivity,

$l=$ length

$A=$ cross sectional area

The resistance of length $4m$ is

$R_1=\rho \frac{4}{2\times 3}=\rho \frac{2}{3}$ (maximum )

The resistance of length $3m$ is

$R_2=\rho \frac{3}{4\times 2}=\rho \frac{3}{8}$

The resistance of length $2m$ is

$R_3=\rho \frac{2}{4\times 3}=\frac{\rho }{6}$ (minimum)

The ratio of maximum and minimum resistance is,

Ratio$=\frac{R_1}{R_3}=4$

$R_1:R_3=4:1$

The correct option is A.