THE REPRESENTATION OF DISTRIBUTED RESISTANCE AND SHUNT CAPACITANCE CIRCUITS BY LUMPED NETWORKS

Lawson, D.I. and McGuire, J.H., 1955. THE REPRESENTATION OF DISTRIBUTED RESISTANCE AND SHUNT CAPACITANCE CIRCUITS BY LUMPED NETWORKS. Fire Research Notes 196

ABSTRACT

The temperature ? at any point in a unidirectional heat conduction problem is given by the application of the appropriate boundary conditions to the equation: (d?/dt) = k(d2?/dx2), where k is the thermal diffusivity of the material considered. The potential difference across a transmission line with distributed series resistance and shunt capacity is given by the application of the appropriate boundary conditions to the equation: (dv/dt) = (1/RC)(d2v/dt2). The similarity between the two equations makes it apparent that the solution of a heat conduction problem may be obtained by solving the analogous electrical problem. It is however not usually practical to construct electrical transmission lines in which the capacity is uniformly distributed and consideration must be given to the representation of such a line by lumped networks. The representation of distributed networks with boundary conditions involving a potential difference have already been dismissed. The present note relates to problems in which the boundary flux is specified.

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