Question

The dimensions of electrical conductivity is

• A. [TA]
• B. [ML\(^3\)T\(^{-3}\)A\(^{-2}\)]
• C. [M\(^{-1}\)L\(^{-3}\)T\(^3\)A\(^2\)]
• D. [MLT\(^{-3}\)A\(^{-1}\)]

Hint:

Conductivity = reciprocal of resistivity, so flip the dimensions of \(\rho\).

Answer 1

The Correct Option is C

Step 1: Conductivity and Resistivity Relationship
Conductivity (\(\sigma\)) is the inverse of resistivity (\(\rho\)): \[\sigma = \frac{1}{\rho}\] Step 2: Resistivity Dimensions
Resistivity is defined as: \[\rho = R \cdot \frac{A}{L}\] where resistance \(R = \frac{V}{I}\). The dimensions of voltage (\(V\)) are: \[[V] = [ML^2T^{-3}A^{-1}]\] Current (\(I\)) has dimensions [A]. Therefore, the dimensions of resistance are: \[[R] = [ML^2T^{-3}A^{-2}]\] Substituting into the resistivity equation: \[[\rho] = [R] \cdot \frac{L^2}{L} = [ML^3T^{-3}A^{-2}]\] Step 3: Determining Conductivity Dimensions
Since conductivity is the inverse of resistivity: \[[\sigma] = [\rho]^{-1} = [M^{-1}L^{-3}T^3A^2]\]
Final Answer: \[ \boxed{[M^{-1}L^{-3}T^3A^2]} \]