To obeserve the effect of concentration on the conductivity, electrolytes of different natures are taken in two vessels `A` and `B,` A contains weak electrolyte, `e.g., NH_(4)OH` and `B` contains strong electrolyte, `e.g., NaCl`. In both containers, the concentration of respective electrolyte is increased and the conductivity observed`:`

Options

A. In `A` conductivity increases, in `B` conductivity decrease
B. In `A` conductivity decreases while, in `B` conductivity decrease
C. In both `A` and `B` conductivity increases
D. In both `A` and `B` conductivity decreases

Explanation

To solve the question regarding the effect of concentration on the conductivity of electrolytes in vessels A and B, we will analyze the behavior of a weak electrolyte (NH₄OH) in vessel A and a strong electrolyte (NaCl) in vessel B as their concentrations are increased.

### Step-by-Step Solution:

1. **Understanding Electrolytes**:
- Electrolytes are substances that dissociate into ions when dissolved in water. They can be classified into two categories: strong electrolytes (which completely dissociate into ions) and weak electrolytes (which partially dissociate).

2. **Identifying the Electrolytes**:
- In vessel A, we have a weak electrolyte: **NH₄OH (Ammonium Hydroxide)**.
- In vessel B, we have a strong electrolyte: **NaCl (Sodium Chloride)**.

3. **Effect of Concentration on Conductivity**:
- Conductivity (κ) of an electrolyte solution is directly proportional to the number of ions present in the solution. More ions lead to higher conductivity.
- As the concentration of an electrolyte increases, the number of ions in the solution increases, which in turn increases the conductivity.

4. **Analyzing Vessel A (NH₄OH)**:
- When the concentration of NH₄OH is increased, more NH₄OH molecules dissociate into NH₄⁺ and OH⁻ ions.
- Since NH₄OH is a weak electrolyte, it does not fully dissociate, but increasing the concentration will still lead to an increase in the number of ions.
- Therefore, the conductivity in vessel A will **increase**.

5. **Analyzing Vessel B (NaCl)**:
- When the concentration of NaCl is increased, NaCl completely dissociates into Na⁺ and Cl⁻ ions.
- As the concentration increases, the number of Na⁺ and Cl⁻ ions in the solution also increases.
- Thus, the conductivity in vessel B will also **increase**.

6. **Conclusion**:
- For both vessels A and B, as the concentration of the respective electrolytes is increased, the conductivity increases.
- Therefore, the correct answer is that in both A and B, the conductivity increases with an increase in concentration.

### Final Answer:
The correct option is **Option 3**: In both A and B, conductivity increases with an increase in concentration.