The Coefficient of Coupling between Two Coils

The coefficient of coupling between two coils is a measure of the magnetic coupling between the coils. It is denoted by the symbol "k" and is a dimensionless quantity ranging from 0 to 1. A coefficient of coupling of 0 indicates no magnetic coupling between the coils, while a coefficient of coupling of 1 indicates maximum magnetic coupling.

Given Parameters:
- Self-inductance of coil 1 (L1) = 16 H
- Self-inductance of coil 2 (L2) = 9 H
- Coefficient of mutual inductance (M) = 9 H

Formula for the Coefficient of Coupling:
The coefficient of coupling can be calculated using the formula:

k = M / √(L1 * L2)

Calculation:
Substituting the given values into the formula, we have:

k = 9 H / √(16 H * 9 H)

Simplifying the expression inside the square root:

k = 9 H / √(144 H^2)

k = 9 H / 12 H

k = 0.75

Explanation:
The coefficient of coupling between the two coils is 0.75. This value indicates a relatively high degree of magnetic coupling between the coils. It implies that a significant amount of magnetic flux generated by one coil will link with the other coil.

Interpretation:
A coefficient of coupling of 0.75 suggests that the two coils are closely placed and have a strong magnetic interaction. This can be advantageous in applications such as transformers and mutual inductors, where the transfer of energy or signals between the two coils is desired.

Conclusion:
In summary, the coefficient of coupling between the two coils with self-inductance values of 16 H and 9 H, and a coefficient of mutual inductance of 9 H, is 0.75. This value signifies a significant magnetic coupling between the coils, indicating a strong interaction between them.