The resistance will be least in a wire with dimensions:

Options

A. `L/3 , 3A`
B. `L/2, 2A`
C. `3L,A`
D. `L,A`

Explanation

To determine which wire has the least resistance based on the given dimensions, we can use the formula for resistance:

\[ R = \frac{\rho L}{A} \]

where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the wire,
- \( A \) is the cross-sectional area of the wire.

### Step-by-Step Solution:

1. **Understand the relationship between resistance, length, and area**:
- From the formula, we see that resistance \( R \) is directly proportional to the length \( L \) and inversely proportional to the area \( A \). This means that if the length increases, the resistance increases, and if the area increases, the resistance decreases.

2. **Analyze the options**:
- We need to evaluate the resistance for each option based on the given dimensions.

3. **Calculate resistance for each option**:
- **Option 1**: Length \( L/3 \), Area \( 3A \)
\[ R_1 = \frac{\rho (L/3)}{3A} = \frac{\rho L}{9A} \]
- **Option 2**: Length \( L/2 \), Area \( 2A \)
\[ R_2 = \frac{\rho (L/2)}{2A} = \frac{\rho L}{4A} \]
- **Option 3**: Length \( 3L \), Area \( A \)
\[ R_3 = \frac{\rho (3L)}{A} = \frac{3\rho L}{A} \]
- **Option 4**: Length \( L \), Area \( A \)
\[ R_4 = \frac{\rho L}{A} \]

4. **Compare the calculated resistances**:
- From the calculations:
- \( R_1 = \frac{\rho L}{9A} \)
- \( R_2 = \frac{\rho L}{4A} \)
- \( R_3 = \frac{3\rho L}{A} \)
- \( R_4 = \frac{\rho L}{A} \)

5. **Determine the least resistance**:
- The smallest value among \( R_1, R_2, R_3, R_4 \) is \( R_1 \) since \( \frac{\rho L}{9A} < \frac{\rho L}{4A} < \frac{3\rho L}{A} < \frac{\rho L}{A} \).

6. **Conclusion**:
- Therefore, the resistance will be least in the wire with dimensions \( L/3 \) and \( 3A \).

### Final Answer:
The resistance will be least in a wire with dimensions \( L/3 \) and \( 3A \) (Option 1).