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: Define conductivity.
Conductivity, written as $\kappa$, tells us how easily a material lets electric current flow through it.
Step 2: Define resistivity.
Resistivity, written as $\rho$, tells us how strongly a material resists the flow of current. It is the opposite idea.
Step 3: Write the link.
The two are simple reciprocals of each other, $\kappa = \dfrac{1}{\rho}$.
Step 4: Read the relationship.
Because one is one over the other, conductivity is inversely proportional to resistivity. When resistivity goes up, conductivity goes down.
Step 5: Reject the wrong options.
It is not directly proportional to resistivity or to resistance, and the molar conductivity link in option 2 is not the basic definition. So those are wrong.
Step 6: Final choice.
Conductivity is inversely proportional to resistivity, which is option 1.
\[ \boxed{\kappa = \dfrac{1}{\rho}} \]