Question

A rectangular parallelopiped is measured as 1 cm × 1 cm × 100 cm. If its specific resistance is 3 × 10^-7 Ωm, then the resistance between its two opposite rectangular faces will be _____ ×10^-7 Ω.

Answer 1

Correct Answer: 3

Step 1: Understanding the formula for resistance.
The resistance \( R \) between two opposite faces of a rectangular parallelepiped is given by the formula: \[ R = \rho \frac{l}{A} \] Where:
\( \rho = 3 \times 10^{-7} \, \Omega \)-cm is the specific resistance,
\( l = 1 \, \text{cm} \) is the length of the parallelepiped,
\( A = 1 \, \text{cm} \times 100 \, \text{cm} = 100 \, \text{cm}^2 \) is the cross-sectional area.
Step 2: Calculating the resistance.
Substituting the given values:
\[ R = \frac{3 \times 10^{-7} \times 1}{100 \, \text{cm}^2} = 3 \times 10^{-7} \times \frac{1}{100 \times 10^{-4}} = 3 \times 10^{-5} \, \Omega \] Thus, the resistance between the two opposite faces is \( 3 \times 10^{-5} \, \Omega \).