Question

Three solenoid coils of same dimension, same number of turns and same number of layers of winding are taken. Coil 1 with inductance \(L_1\) was wound using an A m wire of resistance \(11\Omega/m\); Coil 2 with inductance \(L_2\) was wound using 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 coils \(L_1, L_2, L_3\) are

• A. \(L_1 = L_2 = L_3\)
• B. \(L_1 = L_2;\, L_3 = 0\)
• C. \(L_1 = L_3;\, L_2 = 0\)
• D. \(L_1>L_2>L_3\)

Hint:

Inductance depends on geometry and turns, not on resistance or whether wire is superconducting.

Answer 1

The Correct Option is A

Step 1: Recall factors affecting self-inductance.
Self-inductance depends on geometry of coil:
Number of turns, cross-sectional area, length, and permeability of medium.
\[ L = \frac{\mu N^2 A}{l} \]
Step 2: Compare coil 1 and coil 2.
Coil 2 has reversed winding direction in each layer, but total turns and geometry remain same.
Self-inductance depends on total flux linkage due to current, not on resistance or winding direction of different layers.
So:
\[ L_1 = L_2 \]
Step 3: Effect of superconducting wire on inductance.
Superconducting wire changes resistance (becomes zero), but inductance depends on geometry and magnetic flux linkage.
So:
\[ L_3 = L_1 \]
Step 4: Final conclusion.
All coils have same inductance.
Final Answer:
\[ \boxed{L_1 = L_2 = L_3} \]