Question

The SI unit of conductivity is

• A. Meter
• B. Ohm-meter
• C. Ohm
• D. Siemens per meter (S/m)

Hint:

Units. Resistivity (\(\rho\)): \(\Omega \cdot m\). Conductivity (\(\sigma = 1/\rho\)): \((\Omega \cdot m)^{-1 = \Omega^{-1 \cdot m^{-1\) = S/m (Siemens per meter).

Answer 1

The Correct Option is D

Conductivity (\(\sigma\)) is the reciprocal of resistivity (\(\rho\))
$$ \sigma = \frac{1}{\rho} $$ Resistivity is defined from the relationship \(R = \rho \frac{L}{A}\), where R is resistance, L is length, and A is cross-sectional area
The SI unit of resistance is Ohm (\(\Omega\)), length is meter (m), and area is square meter (m\(^2\))
Therefore, the unit of resistivity \(\rho\) is: $$ \text{Unit}(\rho) = \frac{\text{Unit}(R) \times \text{Unit}(A)}{\text{Unit}(L)} = \frac{\Omega \cdot \text{m}^2}{\text{m}} = \Omega \cdot \text{m} $$ The SI unit of resistivity is Ohm-meter
The SI unit of conductivity is the reciprocal of the unit of resistivity: $$ \text{Unit}(\sigma) = \frac{1}{\text{Unit}(\rho)} = \frac{1}{\Omega \cdot \text{m}} = \Omega^{-1} \cdot \text{m}^{-1} $$ The unit \(\Omega^{-1}\) (reciprocal Ohm) is called Siemens (S)
Therefore, the SI unit of conductivity is Siemens per meter (S/m)