The transformer coupling coefficient k is defined as M / sqrt(L1 L2). Which statement is true?

The transformer coupling coefficient k is defined as M / sqrt(L1 L2). Which statement is true?

• A. 0 ≤ k ≤ 1; higher k reduces leakage inductance; perfect coupling k=1
• B. k can exceed 1
• C. k is always 0
• D. k = sqrt(L1 L2) / M

Answer: (C)

The coupling coefficient describes how well the magnetic flux from one winding links the other. It’s defined as k = M / sqrt(L1 L2), where M is the mutual inductance and L1, L2 are the self-inductances. From the energy and flux constraints in coupled coils, |M| cannot exceed sqrt(L1 L2); thus k must lie between 0 and 1, with k = 1 representing perfect coupling (all flux links both windings) and k = 0 representing no coupling (M = 0). A higher k means less leakage inductance because more of the flux is shared between the windings. The other statements fail because k cannot exceed 1, it is not always zero, and the reciprocal expression would not be the defined form.

The coupling coefficient describes how well the magnetic flux from one winding links the other. It’s defined as k = M / sqrt(L1 L2), where M is the mutual inductance and L1, L2 are the self-inductances. From the energy and flux constraints in coupled coils, |M| cannot exceed sqrt(L1 L2); thus k must lie between 0 and 1, with k = 1 representing perfect coupling (all flux links both windings) and k = 0 representing no coupling (M = 0). A higher k means less leakage inductance because more of the flux is shared between the windings. The other statements fail because k cannot exceed 1, it is not always zero, and the reciprocal expression would not be the defined form.