Series vs Parallel Circuits
In a series circuit components share a single current path. Resistors in series: Rtotal = R1 + R2 + .... Capacitors in series: 1/Ctotal = 1/C1 + 1/C2 + .... If one component opens, the entire circuit goes off (old-style Christmas lights).
In a parallel circuit components share the same voltage but provide independent current paths. Resistors in parallel: 1/Rtotal = 1/R1 + 1/R2 + .... Capacitors in parallel: Ctotal = C1 + C2 + .... Household wiring is parallel so individual loads can be switched independently.
Most real circuits are hybrids analysed by Kirchhoff's voltage and current laws.
Recent research on this topic from arXiv
Preprints and papers indexed on arXiv.org. Links open the public abstract pages.
- Concepts of Electric Circuit Analysis Revised: Analysis without Current Direction
Tomaž Podobnik · 2025 ·arXiv:2501.18609v1
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 la... - Prime, composite and fundamental Kirchhoff graphs
Jessica Wang, Joseph Fehribach · 2022 ·arXiv:2207.11435v1
A Kirchhoff graph is a vector graph with orthogonal cycles and vertex cuts. An algorithm has been developed that constructs all the Kirchhoff graphs up to a fixed edge multiplicity. This algorithm is used to explore the structure of prime K... - The (degree)-Kirchhoff index of linear crossed octagonal-quadrilateral networks
Jia-Bao Liu, Ting Zhang, Wenshui Lin · 2022 ·arXiv:2206.09447v1
The Kirchhoff index and degree-Kirchhoff index have attracted extensive attentions due to its practical applications in complex networks, physics, and chemistry. In 2019, Liu et al. [Int. J. Quantum Chem. 119 (2019) e25971] derived the form... - Resistance distance-based graph invariants of subdivisions and triangulations of graphs
Yujun Yang, Douglas J. Klein · 2014 ·arXiv:1403.1851v1
We study three resistance distance-based graph invariants: the Kirchhoff index, and two modifications, namely, the multiplicative degree-Kirchhoff index and the additive degree-Kirchhoff index. In work in press, one of the present authors (...
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