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 in which case the cell constant is maximum, we first need to understand the definition and formula for the cell constant. The cell constant (k) is defined as the ratio of the distance between the electrodes (L) to the area of cross-section (A) of the electrodes:

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

Now, let's analyze the given cases one by one:

### Case 1:
- Length (L) = 100 cm
- Area (A) = 100 cm²

Calculating the cell constant:
\[ k_1 = \frac{100 \, \text{cm}}{100 \, \text{cm}^2} = 1 \, \text{cm}^{-1} \]

### Case 2:
- Length (L) = 10 cm
- Area (A) = 10 cm²

Calculating the cell constant:
\[ k_2 = \frac{10 \, \text{cm}}{10 \, \text{cm}^2} = 1 \, \text{cm}^{-1} \]

### Case 3:
- Volume = 1 cm³
- We can express this as:
- Length (L) = 1 cm
- Area (A) = 1 cm²

Calculating the cell constant:
\[ k_3 = \frac{1 \, \text{cm}}{1 \, \text{cm}^2} = 1 \, \text{cm}^{-1} \]

### Conclusion:
In all three cases, the cell constant is calculated to be:
- \( k_1 = 1 \, \text{cm}^{-1} \)
- \( k_2 = 1 \, \text{cm}^{-1} \)
- \( k_3 = 1 \, \text{cm}^{-1} \)

Since the cell constant is the same in all cases, we conclude that the cell constant is equal in all the cases provided.

### Final Answer:
The cell constant is maximum in case of all options being equal. Therefore, the answer is **fourth option**: it is equal in all the cases.

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