The constant k is called a coupling coefficient and indicates how much of the flux produced by one coil links the other.
For the ideal transformer in Section 10.7.1 and for the transformer in Section 10.7.2, the coupling coefficient is equal to 1
(all flux links both coils). In air-core transformers, the coupling coefficient is almost always smaller than 1. If the coupling
coefficient is known, the emfs in each coil can be calculated from the self-inductances of the two coils and the coupling
coefficient. For the transformer in Figure 10.13b, but now assuming that k 1, the emfs are