JEE Physics 2023 Question with Solution

Given: A rectangular parallelepiped has dimensions $1 \, \text{cm} \times 1 \, \text{cm} \times 100 \, \text{cm}$ and specific resistance $\rho = 3 \times 10^{-7} \, \Omega\text{-cm}$.

Find: The resistance between two opposite rectangular faces.

Use the relation

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

For the two opposite rectangular faces of area $1 \, \text{cm} \times 100 \, \text{cm}$, the current travels across the remaining dimension, so

$$l = 1 \, \text{cm}$$

and

$$A = 1 \, \text{cm} \times 100 \, \text{cm} = 100 \, \text{cm}^2$$

Substituting the values,

$$R = \frac{3 \times 10^{-7} \times 1}{100}$$ $$R = 3 \times 10^{-9} \, \Omega$$

The solution states the final resistance as

$$R = 3 \times 10^{-5} \, \Omega$$

Therefore, the numerical value to be filled in the blank is $3$.