Three solenoid coils of same dimension, same number of turns and same number of layers of windings are taken. Coil 1 with inductance `L_(1)` was would using a wire of resistance `11Omega//m`, coil 2 with inductance `L_(2)` was wound using the similar wire but the direction of winding was reversed in each layer, coil 3 with inductance `L_(3)` was wound using a superconducting wire. The self-inductance of the coils `L_(1),L_(2)` and `L_(3)` are

Options

A. `L_(1)=L_(2)=L_(3)`
B. `L_(1)=L_(2), L_(3)=0`
C. `l_(1)=l_(3), l_(2)=0`
D. `L_(1)gtL_(2)gtL_(3)`

Explanation

To solve the problem regarding the self-inductance of three solenoid coils, we need to analyze the properties of each coil based on the information provided.

### Step-by-Step Solution:

1. **Understanding Inductance**: The self-inductance \( L \) of a solenoid is given by the formula:
\[ L = \frac{\mu_0 n^2 A l}{l} \]
where:
- \( \mu_0 \) is the permeability of free space,
- \( n \) is the number of turns per unit length,
- \( A \) is the cross-sectional area,
- \( l \) is the length of the solenoid.

2. **Coil 1 (Inductance \( L_1 \))**: This coil is wound with a wire of resistance \( 11 \, \Omega/m \). The inductance \( L_1 \) is determined by the number of turns and the physical dimensions of the coil. Since the dimensions and number of turns are the same as the other coils, we can denote:
\[ L_1 = k \quad \text{(where \( k \) is a constant depending on geometry)} \]

3. **Coil 2 (Inductance \( L_2 \))**: This coil is wound with the same wire, but the direction of winding is reversed in each layer. The self-inductance depends on the number of turns and the geometry, not on the direction of winding. Therefore, the inductance remains the same:
\[ L_2 = k \]

4. **Coil 3 (Inductance \( L_3 \))**: This coil is wound using a superconducting wire. In the case of superconductors, below the critical temperature, the resistance becomes zero, and the inductance can be considered to be zero as well because the current can flow indefinitely without any energy loss. Thus:
\[ L_3 = 0 \]

5. **Conclusion**: From the above analysis, we can summarize the inductances:
- \( L_1 = k \)
- \( L_2 = k \)
- \( L_3 = 0 \)

Thus, we conclude that:
\[ L_1 = L_2 \quad \text{and} \quad L_3 = 0 \]

### Final Answer:
- \( L_1 = L_2 \)
- \( L_3 = 0 \)