Some fundamental properties of networks without mutual inductance

Elementary methods, avoiding the manipulation of determinants, are used to prove theorems, not previously enunciated, on the voltage and current gains obtainable from a resistance network, and to deduce therefrom some properties of the algebraic expressions for the voltages and currents in the network. After a brief survey of known properties of general LRC networks, in terms of the complex frequency variable, ¿, the above results are used to obtain properties of general networks without mutual inductance, and in particular a simpler formulation and proof of some properties of RC networks than were given in a recent paper by Fialkow and Gerst.3 Finally, attention is drawn to a neglected paper of Kirchhoff, in which the foundations of the topology of networks were laid down, and use is made of Kirchhoff´s results to obtain explicit expressions, not involving determinants, for the various network parameters.