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Theory of electric networks: the two-point resistance and impedance

Friday 25th April 2008 - 09:00 to 10:00
INI Seminar Room 1

We present a new formulation of the determination of the resistance and impedance between two arbitrary nodes in an electric network. The formulation applies to networks of finite and infinite sizes. An electric network is described by its Laplacian matrix L, whose matrix elements are real for resistors and complex for impedances. For a resistor network the two-point resistance is obtained in terms of the eigenvalues and eigenvectors of L, and for an impedance network the two-point impedance is given in terms of those of L*L. The formulation is applied to regular lattices and non-orientable surfaces. For networks consisting of inductances and capacitances, the formulation predicts the occurrence of multiple resonances.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons