Walker, Halliday & Resnick — Induction and Inductance: Problem 49

49 Two coils connected as shown in Fig. 30-43 separately have inductances \(L_1\) and \(L_2\). Their mutual inductance is \(M\). (a) Show that this combination can be replaced by a single coil of equivalent inductance given by \(L_{eq} = L_1 + L_2 + 2M\). (b) How could the coils in Fig. 30-43 be reconnected to yield an equivalent inductance of \(L_{eq} = L_1 + L_2 - 2M\)? (This problem is an extension of Problem 11, but the requirement that the coils be far apart has been removed.)