The units of specific conductance `(kappa)` are

Options

A. `"ohm cm"^(-1)`
B. `ohm^(-1) cm`
C. ohm cm
D. `ohm^(-1) cm^(-1)`

Explanation

To find the units of specific conductance (κ), we start by understanding its definition and relationship with resistivity.

### Step-by-Step Solution:

1. **Definition of Specific Conductance (κ)**:
Specific conductance (κ) is defined as the reciprocal of resistivity (ρ). Mathematically, this can be expressed as:
\[ \kappa = \frac{1}{\rho} \]

2. **Understanding Resistivity (ρ)**:
The resistivity (ρ) is related to resistance (R) through the formula:
\[ \rho = R \cdot \frac{A}{L} \]
where:
- \(R\) = resistance in ohms (Ω)
- \(A\) = cross-sectional area in square meters (m²)
- \(L\) = length in meters (m)

3. **Rearranging the Formula**:
From the equation of resistivity, we can express it in terms of resistance:
\[ \rho = R \cdot \frac{A}{L} \]
Therefore, substituting this into the equation for specific conductance gives:
\[ \kappa = \frac{1}{R \cdot \frac{A}{L}} = \frac{L}{R \cdot A} \]

4. **Determining the Units**:
Now, let’s analyze the units:
- The unit of resistance \(R\) is ohms (Ω).
- The unit of area \(A\) is square meters (m²).
- The unit of length \(L\) is meters (m).

Substituting these units into the equation for κ:
\[ \kappa = \frac{\text{meters (m)}}{\text{ohms (Ω)} \cdot \text{meters}^2 (m^2)} = \frac{1}{\Omega \cdot m} \]

5. **Simplifying the Units**:
This can be simplified to:
\[ \kappa = \Omega^{-1} \cdot m^{-1} \]
Since it is common to express specific conductance in terms of centimeters, we can also express it as:
\[ \kappa = \Omega^{-1} \cdot cm^{-1} \]

6. **Final Answer**:
Therefore, the units of specific conductance (κ) are:
\[ \text{Ohm}^{-1} \cdot \text{meter}^{-1} \quad \text{or} \quad \text{Ohm}^{-1} \cdot \text{centimeter}^{-1} \]

### Conclusion:
The correct answer is that the units of specific conductance (κ) are \( \text{Ohm}^{-1} \cdot \text{meter}^{-1} \) or \( \text{Ohm}^{-1} \cdot \text{centimeter}^{-1} \).