Evaluation of hilbert space techniques and lagrange´s method for the analysis of dissipated power in DC circuits

The basic circuit laws of DC circuits are interpreted in this paper by defining suitable functionals in terms of dissipated power. It is then shown that the minimum of dissipated power determined by taking the derivative of these functionals verifies the first Kirchhoff´s law. This allows interpreting the circuit equations by using the second Kirchhoff´s law and the minimum power principles. In order to estimate the extreme values of dissipated power for DC circuits with modifiable parameters, and the relation between the variation in one or all the resistances of the networks and the variation of dissipated power we use the Lagrange´s method. Numerical examples obtained with Mathematica are provided to show the practical applications and comparison between of two proposed principles of DC circuits.