Based on Faraday's law of electromagnetic induction and the existence condition of non-trivial solution to a homogeneous and linear differential system of equations, the equivalent self-inductance of N coupled parallel coils has been derived by uing some algebraic techniques. It can be expressed as the ratio of the determinants of two matrices, with ranks of N and N-1, respectively, and constructed with the self and mutual inductance of those coils. In addition, special conclusions are deduced and/or discussed in detail for three particular cases: 1, the completely uncoupled case, 2, the identical and symmetrical case, and 3, the completely coupled case, which are coincident with the existing results in the references.
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