Cell constant is maximum in case of a:

Options

A. wire of length 100 cm and area 100 `cm^(2)`
B. wire of length 10 cm and area 10 `cm^(2)`
C. one centimeter cube of a material
D. equal in all cases

Answer

To determine the maximum cell constant in the given options, we need to understand the concept of cell constant in electrochemistry. The cell constant (k) is defined as the ratio of the length (l) of the conductive path to the cross-sectional area (A) of that path. The formula for cell constant is:

\[ k = \frac{l}{A} \]

Where:
- \( k \) = cell constant (in cm⁻¹ or m⁻¹)
- \( l \) = length of the conductor (in cm or m)
- \( A \) = cross-sectional area (in cm² or m²)

### Step-by-Step Solution:

1. **Identify the Formula**:
The cell constant is defined as the length of the cell divided by the area of the cross-section.

\[ k = \frac{l}{A} \]

2. **Evaluate Each Option**:
- **Option A**: Length = 100 cm, Area = 100 cm²
\[ k_A = \frac{100 \, \text{cm}}{100 \, \text{cm}^2} = 1 \, \text{cm}^{-1} \]

- **Option B**: Length = 10 cm, Area = 10 cm²
\[ k_B = \frac{10 \, \text{cm}}{10 \, \text{cm}^2} = 1 \, \text{cm}^{-1} \]

- **Option C**: Length = 1 cm, Area = 1 cm²
\[ k_C = \frac{1 \, \text{cm}}{1 \, \text{cm}^2} = 1 \, \text{cm}^{-1} \]

- **Option D**: Equal in all cases
Since all the calculated cell constants are equal (1 cm⁻¹), this option is also valid.

3. **Conclusion**:
Since the cell constants for options A, B, and C are equal, the maximum cell constant is indeed equal in all cases. Therefore, the correct answer is:

**Answer: D (Equal in all cases)**