Question 22.8: Find the total inductance of the series coils in Fig. 22.29.

\text { Coil 1: } \quad L_{1}\overset{\overset{\text {Current vectors leave dot.}}{\swarrow} }{+} M_{12}\underset{\underset{\text {One current vector enters dot, while one leaves.}}{\nwarrow } }{-} M_{13}.

\text { Coil 2: } \quad L_{2}+M_{12}-M_{23}.

\text { Coil 3: } \quad L_{3}-M_{23}-M_{13}.

and

L_{T}=\left(L_{1}+M_{12}-M_{13}\right)+\left(L_{2}+M_{12}-M_{23}\right)+\left(L_{3}-M_{23}-M_{13}\right).

=L_{1}+L_{2}+L_{3}+2 M_{12}-2 M_{23}-2 M_{13}.

Substituting values, we find

L_{T}=5 H +10 H +15 H +2(2 H )-2(3 H )-2(1 H ).

=34 H -8 H = 26 H.