For a strong electrolyte, equivalent conductance increases slowly with dilution and can be expressed by the relationship`: wedge_(m)=wedge^(@)._(m)-Asqrt(c)`
Which electrolyte (s) have same value of `A` ?

Options

A. `NaCl`
B. `CaCl_(2)`
C. `ZnCl_(2)`
D. `MgSO_(4)`

Explanation

To solve the question, we need to identify which electrolytes have the same value of \( A \) in the equation for equivalent conductance:

\[ \Lambda_m = \Lambda_m^0 - A \sqrt{c} \]

where:
- \( \Lambda_m \) is the equivalent conductance at concentration \( c \),
- \( \Lambda_m^0 \) is the equivalent conductance at infinite dilution,
- \( A \) is a constant that depends on the nature of the ions,
- \( c \) is the concentration of the electrolyte.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The equation indicates that as the concentration \( c \) of a strong electrolyte decreases (dilution), the equivalent conductance \( \Lambda_m \) increases. The term \( A \sqrt{c} \) represents the decrease in conductance due to the interactions between ions at higher concentrations.

2. **Identifying the Factors Affecting \( A \)**:
The value of \( A \) is influenced by the charges of the cations and anions present in the electrolyte. Specifically, it depends on the magnitude of the charge of the ions.

3. **Analyzing Given Electrolytes**:
- **NaCl**: Dissociates into \( Na^+ \) and \( Cl^- \) (2 ions total).
- **CaCl2**: Dissociates into \( Ca^{2+} \) and \( 2Cl^- \) (3 ions total).
- **ZnCl2**: Dissociates into \( Zn^{2+} \) and \( 2Cl^- \) (3 ions total).
- **MgSO4**: Dissociates into \( Mg^{2+} \) and \( SO4^{2-} \) (2 ions total).

4. **Comparing the Electrolytes**:
- **CaCl2** and **ZnCl2** both produce 3 ions upon dissociation and contain divalent cations (Ca and Zn) with the same charge as well as two monovalent anions (Cl).
- **NaCl** and **MgSO4** produce different types of ions compared to the other two.

5. **Conclusion**:
Since \( CaCl2 \) and \( ZnCl2 \) have the same number of ions and similar charge characteristics, they will have the same value of \( A \).

### Final Answer:
The electrolytes that have the same value of \( A \) are **CaCl2** and **ZnCl2**.