Cross current of a 5-arm network

This paper treats the loci of cross currents in 5-arm networks with constant coefficients at constant applied voltage. It is shown that at constant frequency of applied voltage, the locus of the cross current is a circle when any one of the network arms is varied at constant phase angle or along one of its components. When the network arms are fixed and the frequency is varied the locus of the cross current is the sum of several circles, the number depending upon how many of the impedance arms vary with frequency. The general 5-arm network is treated analytically and the application of the method in determining the loci is illustrated by a typical network for which the cross current is evaluated for constant and for varying frequency.