Related papers: Experimental determination of circuit equations
The electric current as the flux of current density -- a signed scalar, not a vector -- is inconsistent with the concept of the current direction, commonly invoked in the electric circuit analyses within, for example, Kirchhoff's current…
Direct current (DC) circuits are usually taught in upper-level physics curricula, and Kirchhoff's laws are stated and used to solve the steady-state currents. However, students are not often introduced to alternative techniques, such as…
Kirchhoff's current law is thought to describe the translational movement of charged particles through resistors. But Kirchhoff's law is widely used to describe movements of current through resistors in high speed devices. Current at high…
Students often have difficulty in understanding qualitatively the behaviour of simple electric circuits. In particular, as different studies have shown, they find multiple batteries connected in multiple loops difficult to analyse. In a…
This paper proposes a new analysis of graph using the concept of electric potential, and also proposes a graph simplification method based on this analysis. Suppose that each node in the weighted-graph has its respective potential value.…
We lay the foundation of a circuit theory for chemical reaction networks. Chemical reactions are grouped into chemical modules solely characterized by their current-concentration characteristic, as electrical devices by their…
In this work a classical derivation of fractional order circuits models is presented. Generalized constitutive equations in terms of fractional Riemann-Liouville derivatives are introduced in the Maxwell's equations. Next the Kirchhoff…
In this work, we present novel general analytical solutions for the currents that are developed in the edges of network-like circuits when some nodes of the network act as sources/sinks of DC or AC current. We assume that Ohm's law is valid…
A probabilistic method is derived for solution of ohmic circuit problems. It is compared to the standard approach, which is construction and solution of a set of coupled, linear equations manifesting Kirchhoff's laws. An example is made of…
Use of explicit methods for simulating electrical circuits, especially for power electronics applications, is described. Application of the forward Euler method to a half-wave rectifier is discussed, and the limitations of a fixed-step…
External electric circuits attached to radio-frequency plasma discharges are essential for the power transfer into the discharge and are, therefore, a key element for plasma operation. Many plasma simulations, however, simplify or even…
This paper presents a general framework for linear circuit analysis based on elementary aspects of projective geometry. We use a flexible approach in which no a priori assignment of an electrical nature to the circuit branches is necessary.…
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.…
The methods of abstract simplicial homology and cohomology are reviewed and applied to the topology of electrical networks. Kirchhoffs laws of electrical circuits are shown to be manifestly homological in their origins. Since they are based…
Research has shown that both high school and university students' reasoning patterns regarding direct current resistive electric circuits often differ from the currently accepted explanations. At present, there are no standard diagnostic…
Kirchhoff's Current Law is an essential tool in the design of circuits that operate very quickly, faster than nanoseconds. But Kirchhoff's current is often identified as the flow of particles. The continuity equation or the Maxwell-Ampere…
The analysis conducted by Rymarz and DiVincenzo (Phys. Rev. X 13, 021017 (2023)) regarding quantization of superconducting circuits is insufficient to justify their general conclusions, most importantly the need to discard Kirchhoff's laws…
We present a formulation of general nonlinear LC circuits within the framework of Birkhoffian dynamical systems on manifolds. We develop a systematic procedure which allows, under rather mild non-degeneracy conditions, to write the…
In contrast to the standard derivation of Kirchhoff's loop law, which invokes electric potential, we show, for the linear planar electric network in a stationary state at the fixed temperature,that loop law can be derived from the maximum…
Our digital technology depends on mathematics to compute current flow and design its devices. Mathematics describes current flow by an idealization, Kirchhoff's current law. All the electrons that flow into a node flow out. This…