物理通报
物理通報
물리통보
PHYSICS BULLETIN
2014年
7期
122-127
,共6页
自感%互感%等效自感系数%电磁感应%并联%耦合线圈
自感%互感%等效自感繫數%電磁感應%併聯%耦閤線圈
자감%호감%등효자감계수%전자감응%병련%우합선권
Electromagnetic induction%formula of equivalent self inductance%mutual inductance%coupling coil%parallel coupling circuit
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。
將法拉第電磁感應定律應用于 N 箇相互耦閤的併聯自感線圈，從齊次線性微分方程的非平庸解的存在性條件齣髮，併運用行列式技術，推導齣 N 箇相互耦閤的自感線圈，在併聯情形的等效自感繫數。指齣併聯情形的等效自感繫數是由各自的自感繫數與互感繫數構成的兩箇分彆為 N 階與 N -1階矩陣的行列式之比，給定瞭存在反嚮併聯情形的符號規則；併討論瞭在完全不耦閤、全同對稱、完全耦閤等若榦特例情形的具體結論，結果均與文獻的已有結論相符。
장법랍제전자감응정률응용우 N 개상호우합적병련자감선권，종제차선성미분방정적비평용해적존재성조건출발，병운용행렬식기술，추도출 N 개상호우합적자감선권，재병련정형적등효자감계수。지출병련정형적등효자감계수시유각자적자감계수여호감계수구성적량개분별위 N 계여 N -1계구진적행렬식지비，급정료존재반향병련정형적부호규칙；병토론료재완전불우합、전동대칭、완전우합등약간특례정형적구체결론，결과균여문헌적이유결론상부。
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 .
