What is the permissible range for the coupling coefficient k in mutual inductance?

What is the permissible range for the coupling coefficient k in mutual inductance?

• A. 0 ≤ k ≤ 1
• B. -1 ≤ k ≤ 1
• C. k ≤ 0
• D. k ≥ 0

Answer: (A)

Coupling coefficient measures how completely the magnetic flux from one coil links the other. It is defined as k = M / sqrt(L1 L2), where M is the mutual inductance and L1, L2 are the self-inductances. For the two-coil system to have a physically valid (positive semidefinite) energy, the inductance terms must satisfy L1 L2 - M^2 ≥ 0, which means |M| ≤ sqrt(L1 L2). Dividing by sqrt(L1 L2) gives |k| ≤ 1. Since k is taken as a nonnegative quantity (the magnitude of coupling), the permissible range is 0 ≤ k ≤ 1. Negative M can occur if the winding orientation (dots) produces opposite polarity, but the coupling coefficient itself is defined as a magnitude, so it stays nonnegative.

Coupling coefficient measures how completely the magnetic flux from one coil links the other. It is defined as k = M / sqrt(L1 L2), where M is the mutual inductance and L1, L2 are the self-inductances. For the two-coil system to have a physically valid (positive semidefinite) energy, the inductance terms must satisfy L1 L2 - M^2 ≥ 0, which means |M| ≤ sqrt(L1 L2). Dividing by sqrt(L1 L2) gives |k| ≤ 1. Since k is taken as a nonnegative quantity (the magnitude of coupling), the permissible range is 0 ≤ k ≤ 1. Negative M can occur if the winding orientation (dots) produces opposite polarity, but the coupling coefficient itself is defined as a magnitude, so it stays nonnegative.