All the edges of a block with parallel faces are unequal. Its longest edge is twice its shortest edge. The ratio of the maximum to minimum resistance between parallel faces is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
Between two parallel faces, \( R=\rho l/A \). Here the length \( l \) is the edge along the current, and \( A \) is the area of the face.
The resistance is maximum when the current runs along the longest edge (the smallest face).
It is minimum when the current runs along the shortest edge (the largest face).
Let the edges be \( a \), \( b \) and \( 2a \).
\( \begin{aligned} R_{\max} &= \frac{\rho\,(2a)}{a\,b} \\ &= \frac{2\rho}{b} \end{aligned} \)
\( \begin{aligned} R_{\min} &= \frac{\rho\,a}{(2a)\,b} \\ &= \frac{\rho}{2b} \end{aligned} \)
\( \begin{aligned} \frac{R_{\max}}{R_{\min}} &= \frac{2\rho/b}{\rho/2b} \\ &= 4 \end{aligned} \)