The unit of cell constant is:

Options

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

Answer

To find the unit of cell constant, we can follow these steps:

### Step 1: Understand the Concept of Cell Constant
The cell constant is a term used in electrochemistry, particularly in relation to the resistance of a conductor. It is defined as the ratio of the length of the conductor to its cross-sectional area.

### Step 2: Define Resistance
Resistance (R) is the opposition that a conductor offers to the flow of electric current. It is directly proportional to the length (L) of the conductor and inversely proportional to its cross-sectional area (A).

### Step 3: Write the Formula for Resistance
The relationship can be expressed mathematically as:
\[ R = \rho \frac{L}{A} \]
where:
- \( R \) = resistance,
- \( \rho \) = resistivity (a constant),
- \( L \) = length of the conductor,
- \( A \) = cross-sectional area.

### Step 4: Identify the Cell Constant
From the formula, the term \( \frac{L}{A} \) is referred to as the cell constant (k).

### Step 5: Determine the Units
- The unit of length (L) is measured in centimeters (cm).
- The unit of area (A) is measured in square centimeters (cm²).

### Step 6: Calculate the Unit of Cell Constant
To find the unit of cell constant, we substitute the units into the expression:
\[ \text{Unit of Cell Constant} = \frac{\text{cm}}{\text{cm}^2} = \text{cm}^{-1} \]

### Conclusion
The unit of cell constant is \( \text{cm}^{-1} \).

### Final Answer
The correct answer is option **d) centimeter inverse (cm⁻¹)**.

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