Two resistors A and B have resistances `R_(A) and R_(B)`respectively with `R_(A)ltR_(B)`.the resistivities of their materials are `(rho_A) and (rho_B)`.

Options

A. (a)`(rho_A) gt(rho_B)`
B. (b)`(rho_A)=(rho_B)`
C. (c ) `(rho_A)lt(rho_B)`
D. (d) the information is not sufficient to find the relation between `(rho_A)and(rho_B)`

Answer

To solve the problem regarding the resistors A and B, we will analyze the given information step by step.

### Step-by-Step Solution:

1. **Understanding Resistance**:
The resistance \( R \) of a conductor can be expressed using the formula:
\[ R = \frac{\rho \cdot L}{A} \]
where \( \rho \) is the resistivity of the material, \( L \) is the length of the conductor, and \( A \) is the cross-sectional area.

2. **Given Information**:
We know that:
- Resistance of A: \( R_A \)
- Resistance of B: \( R_B \)
- It is given that \( R_A < R_B \).

3. **Relating Resistances to Resistivities**:
Since we have two resistors, we can write their resistances as:
\[ R_A = \frac{\rho_A \cdot L_A}{A_A} \]
\[ R_B = \frac{\rho_B \cdot L_B}{A_B} \]
Here, \( \rho_A \) and \( \rho_B \) are the resistivities of materials A and B respectively, while \( L_A, L_B \) are their lengths and \( A_A, A_B \) are their cross-sectional areas.

4. **Analyzing the Comparison**:
Since \( R_A < R_B \), we can write:
\[ \frac{\rho_A \cdot L_A}{A_A} < \frac{\rho_B \cdot L_B}{A_B} \]
However, without additional information about the lengths and cross-sectional areas of the resistors, we cannot directly compare the resistivities \( \rho_A \) and \( \rho_B \).

5. **Conclusion**:
The problem does not provide sufficient information to determine the relationship between the resistivities \( \rho_A \) and \( \rho_B \). Therefore, we cannot conclude whether \( \rho_A > \rho_B \), \( \rho_A < \rho_B \), or \( \rho_A = \rho_B \).

### Final Answer:
The answer is that there is insufficient information to determine the relationship between the resistivities \( \rho_A \) and \( \rho_B \).

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