Related papers: The two capacitor problem revisited: simple harmon…
The classical two-capacitor problem shows a mysterious lose of energy even under lossless conditions and questions the basic understanding of energy relation in a capacitor. Here, we present a solution to the classical two-capacitor…
In this work we suggest very simple solution of the two capacitors paradox in the completely ideal (without any electrical resistance or inductive) electrical circuit. Namely, it is shown that electrical field energy loss corresponds to…
It is shown that the famous paradox of two charged capacitors is successfully resolved if all the energy changes in the system are properly considered when some of the charges are transferred from one capacitor to the other. It happens so…
Approximate formulas are derived to describe energy loss in a harmonic oscillator that experiences three distinct damping mechanisms: constant-magnitude (Coulomb), velocity-proportional (Stokes), and velocity-squared (Newton), using…
In the present work we study the well-known Two Capacitor Problem from a new perspective. Although this problem has been thoroughly investigated, as far as we know there are no studies of the thermodynamic aspects of the discharge process.…
We demonstrate how to derive the exponential decrease of amplitude and an excellent approximation of the energy decay of a weakly damped harmonic oscillator without solving the associated equation of motion and without insight into the…
Inspired by recent assertions that imply incorrectness of the classical constitutive relationship of time-varying capacitance, energetic and system-theoretic perspectives are invoked that, instead of incorrectness, show incompleteness of…
Half of the energy is always lost when charging a capacitor. Even in the limit of vanishing resistance, half of the charging energy is still lost--to radiation instead of heat. While this fraction can technically be reduced by charging…
Capacitors are ubiquitous in electronic and electrical devices. In this article, we study -- both theoretically and experimentally -- the charging and discharging of capacitors using active control of a voltage source. The energy of these…
The Casimir friction problem can be dealt with in a simplified way by considering two harmonic oscillators moving with constant relative velocity. Recently we calculated the energy dissipation for such a case, [EPL {\bf 91}, 60003 (2010);…
Assuming that a constant potential energy function has meaning for a dissipated harmonic oscillator, then an important issue is the time dependence of the turning points. Turning point studies demonstrate that the common model of external…
We analyze a category of problems that is of interest in many physical situations, including those encountered in introductory physics classes: systems with two well-delineated parts that exchange energy, eventually reaching a shared…
Consider two capacitors in parallel, but initially isolated by a switch such that one is charged and the other not. After the switch is closed, the charges redistribute themselves in such a way that the final electrostatic energy is less…
We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…
We reveal a new face of the old clich\'ed system: a dissipative quantum harmonic oscillator. We formulate and study a quantum counterpart of the energy equipartition theorem satisfied for classical systems.Both mean kinetic energy $E_k$ and…
We present a systematic analysis and classification of several models of quantum batteries involving different combinations of two level systems and quantum harmonic oscillators. In particular, we study energy transfer processes from a…
We discuss how to connect the energy levels of two-particle systems trapped by a harmonic-oscillator force to scattering amplitudes, with nucleon-nucleon scattering phase shifts in uncoupled channels as the application. At the center of the…
The classical two-capacitor paradox of the lost energy is revisited from an electronic circuit security stand-point. The paradox has been solved previously by various researchers, and the energy lost during the charging of capacitors has…
In this chapter we treat the quantum damped harmonic oscillator, and study mathematical structure of the model, and construct general solution with any initial condition, and give a quantum counterpart in the case of taking coherent state…
The split-charge equilibration method is extended to describe dissipative charge transfer similarly as the Drude model, whereby the generic frequency-dependent dielectric permitivitties or conductivities of dielectrics and metals can be…