Kirchhoff voltage law corrected for radiating circuits

TL;DR

This paper revises Kirchhoff's voltage law to include radiative energy losses in oscillating RLC circuits, providing a more accurate model of real circuits by accounting for electromagnetic radiation effects.

Contribution

It introduces a modified Kirchhoff law incorporating radiative losses as an effective resistance, enhancing the accuracy of circuit analysis involving radiation.

Findings

Radiative losses can be modeled as an effective resistance.

The radiation spectrum pattern varies with effective and electrical resistance.

The modified law better predicts circuit behavior with radiation effects.

Abstract

When a circular loop composed by a RLC is put to oscillate, the oscillation will eventually vanish in an exponentially decaying current, even considering superconducting wires, due to the emission of electric and magnetic dipole radiation. In this work we propose a modification on the Kirchhoff voltage law by adding the radiative contributions to the energy loss as an effective resistance, whose value is relatively small when compared to typical resistance value, but fundamental to describe correctly real circuits. We have also analysed the change in the pattern of the radiation spectra emitted by the circuit as we vary both the effective and electrical resistance.