Final answer:
The inductance of Coil 1 is 128 mH and the inductance of Coil 2 is 8 mH.
Step-by-step explanation:
The inductance of a coil is given by the formula:
L = (μ * N² * A) / l
Where:
- L is the inductance
- N is the number of turns in the coil
- A is the cross-sectional area of the coil
- l is the length of the coil
- μ is the permeability of free space
In this case, we have two coils, Coil 1 and Coil 2. Given that Coil 1 has twice the number of turns as Coil 2, we can denote the number of turns as N₁ = 2N₂.
Since the mutual inductance between the coils is given as 32 mH and the relative permeability (μ) is 1, we can use the formula:
M = √(L₁ * L₂)
Substituting in the given values and solving for the inductance of each coil, we get:
L₁ = 32 mH * (2²) = 128 mH
L₂ = 32 mH / (2²) = 8 mH