Question

What is the common unit of conductivity if the dimensions are expressed in centimeter?

• A. \(\Omega \, \text{cm}^{-1}\)
• B. \(\Omega^{-1} \, \text{cm}^{-1}\)
• C. \(\Omega \, \text{cm}\)
• D. \(\Omega^{-1} \, \text{cm}\)

Hint:

The unit of conductivity is \(\Omega^{-1} \, \text{cm}^{-1}\) when expressed in centimeter.

Answer 1

The Correct Option is B

Step 1: Understanding Conductivity.
The unit of conductivity is the reciprocal of resistance. If resistance is measured in ohms (\(\Omega\)), then conductivity has units of \(\Omega^{-1}\). Additionally, conductivity is typically measured per unit length (centimeter), which gives the unit \(\Omega^{-1} \, \text{cm}^{-1}\).

Step 2: Analyzing the options.
(A) \(\Omega \, \text{cm}^{-1}\): Incorrect. This represents a unit of resistivity, not conductivity.
(B) \(\Omega^{-1} \, \text{cm}^{-1}\): Correct. This is the correct unit for conductivity when expressed in terms of centimeter.
(C) \(\Omega \, \text{cm}\): Incorrect. This represents a unit of resistivity, not conductivity.
(D) \(\Omega^{-1} \, \text{cm}\): Incorrect. This unit does not correctly represent conductivity.

Step 3: Conclusion.
The correct unit for conductivity is \(\Omega^{-1} \, \text{cm}^{-1}\), corresponding to option (B).