Question

What is the relation between cell constant, conductivity, and electrical resistance?

• A. \( k = \frac{R}{b} \)
• B. \( k = \frac{b}{R} \)
• C. \( k = \frac{1}{R \cdot b} \)
• D. \( k = R \cdot b \)

Hint:

The cell constant \( k \) can be calculated by knowing the resistance \( R \) and the length \( b \) of the cell. The correct relation is \( k = \frac{b}{R} \).

Answer 1

The Correct Option is B

Step 1: Understanding the formula.
The cell constant \( k \) is related to the electrical resistance \( R \), the cell length \( b \), and the conductivity. The cell constant \( k \) is defined as the ratio of the distance between the electrodes (length) to the area of the electrodes. The relation is given by: \[ k = \frac{b}{R} \] Where: - \( b \) is the length of the cell, and - \( R \) is the electrical resistance.
Step 2: Analyzing the options.
(A) \( k = \frac{R}{b} \): This is incorrect because it does not accurately represent the relationship between the conductivity and resistance.
(B) \( k = \frac{b}{R} \): This is correct. The correct relation between the cell constant, conductivity, and electrical resistance is \( k = \frac{b}{R} \), where \( b \) is the cell length and \( R \) is the resistance.
(C) \( k = \frac{1}{R \cdot b} \): This is incorrect, as it does not align with the proper relationship.
(D) \( k = R \cdot b \): This is also incorrect.
Step 3: Conclusion.
The correct answer is (B) \( k = \frac{b}{R} \).