Question

Which of the following represents resistance, R?
\( \rho = \text{resistivity}, l = \text{length of material}, A = \text{cross-sectional area} \)

• A. \( \rho \cdot \left( \frac{1}{A} \right) \)
• B. \( \rho \cdot \left( \frac{A}{l} \right) \)
• C. \( \frac{1}{\rho A} \)
• D. \( \frac{lA}{\rho} \)

Hint:

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

Answer 1

The Correct Option is A

Step 1: Formula for Resistance.
The formula for the resistance \( R \) of a conductor is given by: \[ R = \rho \cdot \frac{l}{A} \] Where: - \( R \) is the resistance - \( \rho \) is the resistivity - \( l \) is the length of the conductor - \( A \) is the cross-sectional area
Step 2: Elimination of options.
- (A) \( \rho \cdot \left( \frac{1}{A} \right) \): This is incorrect because the formula for resistance involves \( \frac{l}{A} \), not \( \frac{1}{A} \).
- (B) \( \rho \cdot \left( \frac{A}{l} \right) \): Incorrect, this would result in a reversed formula.
- (C) \( \frac{1}{\rho A} \): Incorrect, as the formula involves \( \frac{l}{A} \), not \( \frac{1}{A} \).
- (D) \( \frac{lA}{\rho} \): Incorrect, this expression does not correspond to the correct formula for resistance.
Step 3: Conclusion.
Therefore, the correct formula for resistance is \( R = \rho \cdot \frac{l}{A} \).