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: Relation between conductivity and resistivity.
Conductivity (\(\sigma\)) is reciprocal of resistivity (\(\rho\)): \[ \sigma = \frac{1}{\rho} \] Step 2: Dimensions of resistivity.
Resistivity: \[ \rho = R \cdot \frac{A}{L} \] where resistance \(R = \frac{V}{I}\). Voltage (\(V\)) has dimensions: \[ [V] = [ML^2T^{-3}A^{-1}] \] Current (\(I\)) = [A]. So, \[ [R] = [ML^2T^{-3}A^{-2}] \] Now, \[ [\rho] = [R] \cdot \frac{L^2}{L} = [ML^3T^{-3}A^{-2}] \] Step 3: Conductivity.
\[ [\sigma] = [\rho]^{-1} = [M^{-1}L^{-3}T^3A^2] \]
Final Answer: \[ \boxed{[M^{-1}L^{-3}T^3A^2]} \]