Question

A conductor with rectangular cross-section has dimensions $(a\times 2a\times 4a)$ as shown in figure. Resistance across AB is $R_1$, across CD is $R_2$ and across EF is $R_3$. Then which of the following is true?

• A. $R_1=R_2=R_3$
  
• B. $R_1$ > $R_2$ > $R_3$
  
• C. $R_2$ > $R_3$ > $R_1$
  
• D. $R_1$ > $R_3$ > $R_2$

Answer 1

The correct option is B $R_1$ > $R_2$ > $R_3$


Resistance $R=\rho \frac{l}{A}$
From the figure the dimensions are $a$, $2a$ and $4a$, i.e.
Distance between faces A and B = $4a$
Distance between faces C and D= $2a$
Distance between faces E and F= $a$

As $R\propto l$, AB having the highest length will have the most resistance followed by CD and EF being of the lowest length will have the least resistance. So, the order is $R_1>R_2>R_3$.