Calculate the coefficient of coupling between two coils, given that the mutual inductance (M) is 1.5 H and the self inductances are 5 H and 4 H.
Answer (2)
The coefficient of coupling (k) between the two coils is approximately 0.335, indicating that about 33.5% of the magnetic flux from one coil links with the other. This was calculated using the formula k = L 1 ⋅ L 2 M with the given values for mutual and self-inductances. The result shows the effectiveness of energy transfer between the coils.
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To calculate the coefficient of coupling (k) between two coils, we use the relationship between mutual inductance (M), self-inductance of the first coil (L1), and self-inductance of the second coil (L2). The formula for the coefficient of coupling is given by:
k = L 1 ⋅ L 2 M
Given:
Mutual inductance, M = 1.5 H
Self-inductance of the first coil, L 1 = 5 H
Self-inductance of the second coil, L 2 = 4 H
Now we can substitute these values into the formula:
k = 5 ⋅ 4 1.5
Calculate the product inside the square root:
L 1 ⋅ L 2 = 5 ⋅ 4 = 20
Now, calculate the square root:
20 = 4 ⋅ 5 = 2 5 ≈ 4.47
Finally, calculate the coefficient of coupling:
k = 4.47 1.5 ≈ 0.336
Thus, the coefficient of coupling between the two coils is approximately 0.336. This means that about 33.6% of the magnetic flux created by one coil links to the other coil. The value of the coefficient of coupling ranges from 0 to 1, where 1 signifies perfect coupling and 0 signifies no coupling at all.
