Compare the inductances L1 and L2 of two coils if, at the same current strength, the energy

Compare the inductances L1 and L2 of two coils if, at the same current strength, the energy of the magnetic field created by the current in the first coil is 9 times greater than the energy of the magnetic field created by the current in the second coil.

Let’s write the formula for the magnetic field energy of the coil:

W = LI ^ 2/2;

where W is the energy of the magnetic field,

L – inductance of the coil,

I is the current in the coil.

Let us express the inductance of the coil:

L = 2W / I ^ 2

Coil inductance ratio:

L1 / L2 = (2W * 9 / I ^ 2) / (2W / I ^ 2) = 9.

Accordingly, the inductance of the first coil is 9 times greater than the inductance of the second.

Answer: I1 is 9 times more than I2.