Question

Dimensions of a block are \( 1 \, \text{cm} \times 1 \, \text{cm} \times 100 \, \text{cm} \). If the specific resistance of its material is \( 3 \times 10^{-7} \, \Omega \, \text{m} \), then the resistance between the opposite rectangular faces is:

• A. \( 3 \times 10^7 \, \Omega \)
• B. \( 3 \times 10^9 \, \Omega \)
• C. \( 3 \times 10^5 \, \Omega \)
• D. \( 3 \times 10^3 \, \Omega \)

Hint:

Resistance is directly proportional to the length and inversely proportional to the cross-sectional area of the material.

Answer 1

The Correct Option is A

Step 1: Use the formula for resistance.
The resistance of a block is given by: \[ R = \rho \frac{L}{A} \] where \( \rho \) is the resistivity, \( L \) is the length, and \( A \) is the cross-sectional area.
Step 2: Calculate the resistance.
Substituting the values into the formula, we find that the resistance between the opposite rectangular faces is \( 3 \times 10^7 \, \Omega \).
Final Answer: \[ \boxed{3 \times 10^7 \, \Omega} \]