IDENTIFICATION OF RESISTORS IN ELECTRICAL NETWORKS

The purpose of this work is to identify the internal structure of the electrical networks with data obtained from only a part of network or the boundary of network. To be precise, it is discussed whether we can identify resistors or electrical conductivities of each link inside networks by the measurement of voltage on the boundary which is induced by a prescribed current on the boundary. As a result, it is shown that the structure of the resistor network can be determined uniquely by only one pair of the data (current, voltage) on the boundary, if the resistors satisfy an appropriate condition. Besides, several useful results about the energy functionals, which means the electrical power, are included.