Current loci in the general linear A-C network

OUR PROBLEM is to find the way in which the currents and voltages vary in a general linear a-c network connected to a single adjustable branch, when the current of that branch is adjusted under some given restriction. In a general linear network, each branch has a fixed impedance; and the impressed voltages and currents (of which there may be any number, but usually is only one) are also fixed.^∗ The impressed voltages and currents are supposed sinusoidal and of the same frequency; and we are concerned only with the steady state. So all voltages and currents are sinusoidal and may be represented analytically by complex numbers and graphically by plane vectors.