Question

Which among the following statements is true for conductivity?

• A. It is inversely proportional to resistivity.
• B. It is inversely proportional to molar conductivity.
• C. It is directly proportional to resistivity.
• D. It is directly proportional to resistance.

Hint:

Remember these definitions as pairs to avoid confusion: Conductance ($G$) is the mathematical inverse of Resistance ($R$). Conductivity ($\kappa$) is the mathematical inverse of Resistivity ($\rho$).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question tests the fundamental definition and mathematical relationship of electrical conductivity in a solution or material.

Step 2: Key Formula or Approach:
Resistance ($R$) is directly proportional to length ($l$) and inversely proportional to the cross-sectional area ($A$): $R = \rho \frac{l}{A}$, where $\rho$ is the resistivity.
Conductivity ($\kappa$, kappa) is formally defined as the reciprocal of resistivity ($\rho$).

Step 3: Detailed Explanation:
The mathematical expression relates conductivity directly to resistivity:
$$\kappa = \frac{1}{\rho}$$
This equation clearly demonstrates that conductivity ($\kappa$) is inversely proportional to resistivity ($\rho$). As a material's ability to resist current flow (resistivity) increases, its ability to conduct current (conductivity) decreases, and vice versa.

Step 4: Final Answer:
Conductivity is inversely proportional to resistivity, making option (A) the correct statement.