The cell constant is the product of resistance and

Options

A. conductance
B. molar conductance
C. specific conductance
D. specific resistance

Answer

To solve the question "The cell constant is the product of resistance and...", we need to understand the relationship between cell constant, resistance, and conductivity. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Understanding Cell Constant**:
The cell constant (denoted as \( k \)) is defined as the ratio of the distance between the electrodes (length, \( L \)) to the cross-sectional area of the electrodes (area, \( A \)). Mathematically, it is expressed as:
\[ k = \frac{L}{A} \]

2. **Resistance Relation**:
The resistance (\( R \)) of a conductor can be expressed using the formula:
\[ R = \frac{\rho L}{A} \]
where \( \rho \) is the resistivity of the material.

3. **Relating Conductivity**:
The conductivity (\( \kappa \)) is the reciprocal of resistivity:
\[ \kappa = \frac{1}{\rho} \]
Therefore, we can express resistivity in terms of conductivity:
\[ \rho = \frac{1}{\kappa} \]

4. **Substituting Conductivity into Resistance**:
By substituting the expression for \( \rho \) into the resistance formula, we get:
\[ R = \frac{\left(\frac{1}{\kappa}\right) L}{A} = \frac{L}{\kappa A} \]

5. **Finding the Cell Constant in Terms of Resistance**:
Rearranging the equation for resistance gives:
\[ \kappa = \frac{L}{R A} \]
Now, substituting \( k = \frac{L}{A} \) into this equation, we can express the cell constant in terms of resistance:
\[ k = \kappa R \]

6. **Final Conclusion**:
Therefore, we conclude that the cell constant is the product of resistance and specific conductivity:
\[ \text{Cell constant} = \text{Resistance} \times \text{Specific Conductivity} \]

### Final Answer:
The cell constant is the product of resistance and specific conductivity.