Question

A Conductor with rectangular cross-section has dimensions $(a\times 2a\times 4a)$ as shown in figure. Resistance across $\text{AB}$ is $x,$ across $\text{CD}$ is $y$ and across $\text{EF}$ is $z.$ Then

• A. $x=y=z$
• B. $x>y>z$
• C. $y>z>x$
• D. $x>z>y$

Answer 1

The correct option is D $x>z>y$

Formula of resistance is

$R=\frac{\text{Resistivity}\times \text{length}}{\text{Area of cross-section}}=\frac{\rho l}{A}$

Length $l$ is along the direction of flow of current.
Area $A$ is perpendicular to direction of flow of current.

For resistance across $\text{AB}:$

$A=2a^2;l=4a$

$R_{AB}=\frac{\rho \times 4a}{2a^2}=\frac{2\rho }{a}=x$

Similarly,

$R_{CD}=\frac{\rho \times a}{8a^2}=\frac{\rho }{8a}=y$

$R_{EF}=\frac{\rho \times 2a}{4a^2}=\frac{\rho }{2a}=z$

From above expression, we get

$x>z>y$

Hence, option $\left(d\right)$ is correct.

$\begin{array}{c}\text{Why this Question ?}\\ \text{Same piece of a conductor can have different}\\ \text{resistances depending on the points}\\ \text{between which we have to find.}\end{array}$