What does the coupling coefficient k indicate in a transformer, and how does a low k affect performance?

What does the coupling coefficient k indicate in a transformer, and how does a low k affect performance?

• A. Measures winding resistance.
• B. Measures how well flux links both windings; low k increases leakage and reduces efficiency and regulation.
• C. Represents the frequency of operation.
• D. Determines the voltage ratio.

Answer: (B)

The coupling coefficient k tells you how well the magnetic flux produced by one winding links the other. In an ideal transformer, every flux line links both windings, so k equals 1. In real transformers, some flux leaks away and does not link the secondary, so k is less than 1. Because the mutual inductance M is proportional to k (specifically M = k times the geometric mean of the self-inductances), a lower k means less energy is effectively transferred between windings. With reduced coupling, leakage inductance grows, increasing the impedance seen by the secondary and causing the output voltage to sag more under load (poorer voltage regulation). To deliver the same load, the primary must supply more current to overcome the leakage, which raises copper losses and lowers overall efficiency. In short, a low coupling coefficient indicates more leakage flux and degraded transfer performance, reflected in worse efficiency and regulation.

The coupling coefficient k tells you how well the magnetic flux produced by one winding links the other. In an ideal transformer, every flux line links both windings, so k equals 1. In real transformers, some flux leaks away and does not link the secondary, so k is less than 1. Because the mutual inductance M is proportional to k (specifically M = k times the geometric mean of the self-inductances), a lower k means less energy is effectively transferred between windings.

With reduced coupling, leakage inductance grows, increasing the impedance seen by the secondary and causing the output voltage to sag more under load (poorer voltage regulation). To deliver the same load, the primary must supply more current to overcome the leakage, which raises copper losses and lowers overall efficiency. In short, a low coupling coefficient indicates more leakage flux and degraded transfer performance, reflected in worse efficiency and regulation.