Kirchhoff voltage law corrected for radiating circuits

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.