Which of the following relations are not correct ?

Options

A. `Lambda_(m) = (kappa xx 1000)/(M)`
B. `kappa = C xx (a)/(l)`
C. `R = rho "" l/a`
D. `l/a` (cell constant) = `kappa xx (1)/(R)`

Answer

To determine which of the given relations (A, B, C, D) are not correct, we will analyze each relation step by step.

### Step 1: Analyze Relation A
**Relation A:** \( \lambda_m = \kappa \times \frac{1000}{m} \)

- Here, \( \lambda_m \) is the molar conductivity, \( \kappa \) is the specific conductance, and \( m \) is the molarity.
- The formula for molar conductivity is indeed given by \( \lambda_m = \kappa \times \frac{1000}{m} \).
- **Conclusion:** This relation is correct.

### Step 2: Analyze Relation B
**Relation B:** \( \kappa = \text{Conductance} \times \frac{A}{L} \)

- In this relation, \( A \) is the area of cross-section and \( L \) is the length of the electrodes.
- The correct relation is \( \kappa = \text{Conductance} \times \frac{L}{A} \).
- Here, the relation \( \frac{A}{L} \) is incorrect.
- **Conclusion:** This relation is incorrect.

### Step 3: Analyze Relation C
**Relation C:** \( R = \rho \times \frac{L}{A} \)

- Here, \( R \) is resistance, \( \rho \) is resistivity, \( L \) is the length, and \( A \) is the area of cross-section.
- The relation \( R = \rho \times \frac{L}{A} \) is indeed correct.
- **Conclusion:** This relation is correct.

### Step 4: Analyze Relation D
**Relation D:** \( \frac{L}{A} = \kappa \times \frac{1}{R} \)

- The cell constant \( \frac{L}{A} \) is related to conductivity \( \kappa \) and conductance.
- The correct relation is \( \frac{L}{A} = \frac{\kappa}{\text{Conductance}} \), and since Conductance is the reciprocal of resistance, we have \( \text{Conductance} = \frac{1}{R} \).
- Therefore, \( \frac{L}{A} = \kappa \times R \) is the correct relation, not \( \kappa \times \frac{1}{R} \).
- **Conclusion:** This relation is incorrect.

### Final Conclusion
The relations that are not correct are:
- **B:** \( \kappa = \text{Conductance} \times \frac{A}{L} \)
- **D:** \( \frac{L}{A} = \kappa \times \frac{1}{R} \)

### Summary of Incorrect Relations
- **Incorrect Relations:** B and D