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)`

Answer

B

Explanation

The self-inductance of a coil, `L=mu_90)n^(2)Sl`, where `mu_(0)=` permeability of air,
n = number of turns per unit length,
S = area of cross-section and
l = length of the solenoid
This depends on the geometry of inductor such as cross-sectional area, length and number of turns and not on the material, even if it is made of a superconducting material. If the superconductor is below the critical temperature, then the current will continuously flow and the inductance may not have the property of inductance any more.
`therefore" "L_(1)=L_(2')L_(3)=0`