Conductivity `kappa`, is equal to ____

Options

A. `wedge_(m)`
B. `(G^('))/(r)`
C. `(l)/(A)`
D. All of the above

Explanation

To solve the question regarding the conductivity \( \kappa \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Conductivity**:
- Conductivity, denoted by \( \kappa \), is also known as specific conductance. It measures a material's ability to conduct electric current.

2. **Units of Conductivity**:
- The unit of conductivity \( \kappa \) is Siemens per centimeter (S/cm).

3. **Relationship with Conductance**:
- Conductivity \( \kappa \) can be expressed in terms of conductance \( G \) and the cell constant \( G^* \) (or \( G' \)):
\[ \kappa = G \cdot G^* \]

4. **Understanding Conductance and Resistance**:
- Conductance \( G \) is the reciprocal of resistance \( R \):
\[ G = \frac{1}{R} \]
- Therefore, we can rewrite the expression for conductivity as:
\[ \kappa = \frac{1}{R} \cdot G^* \]

5. **Defining Cell Constant**:
- The cell constant \( G^* \) is defined as the ratio of the length \( L \) of the conductor to its cross-sectional area \( A \):
\[ G^* = \frac{L}{A} \]

6. **Final Expression**:
- Combining these relationships, we find that:
\[ \kappa = \frac{G^*}{R} \]
- This indicates that conductivity \( \kappa \) is equal to the cell constant \( G^* \) divided by the resistance \( R \).

### Conclusion:
Thus, the answer to the question "Conductivity \( \kappa \), is equal to ____" is:
\[ \kappa = \frac{G^*}{R} \]