中文摘要：

将法拉第电磁感应定律应用于N个相互耦合的并联自感线圈,从齐次线性微分方程的非平庸解的存在性条件出发,并运用行列式技术,推导出N个相互耦合的自感线圈,在并联情形的等效自感系数.指出并联情形的等效自感系数是由各自的自感系数与互感系数构成的两个分别为N阶与N-1阶矩阵的行列式之比,给定了存在反向并联情形的符号规则;并讨论了在完全不耦合、全同对称、完全耦合等若干特例情形的具体结论,结果均与文献的已有结论相符.

英文摘要：

Based upon 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 coefficient of N coupled parallel coils has been derived by use of some algebraic techniques .It can be expressed as the ratio of the determinants of two matrices ,with ranks of N and N - 1 respectively ,constructed with the self inductance and mutual inductance coefficients of those coils .M eanwhile ,special conclusions are deduced and discussed in detail about 1 ,the com pletely non coupled case ;2 ,the identical and sym metrical case ,and 3 ,the completely coupled case ,which are coincident with the existent results in the references .