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
$\text{Let longest edge is 2L , Shortest edge is L}$.
$\text{Resistivity} = \rho$ ,$Thickness = t$
$\text{Maximum Area} = 2Lt$ , $\text{Minimum area} = Lt$
$ R_{max} = \frac{\rho.L_{max}}{A_{min}} = \frac{\rho.2L}{L.t} = \frac{2\rho}{t}$
$ R_{min} = \frac{\rho.L_{min}}{A_{min}} = \frac{\rho.L}{2L.t} = \frac{\rho}{2t}$
$\Rightarrow \frac{R_{max}}{R_{min}} = 4$