Editing Lumped-element model (section)

=== Lumped-matter discipline ===
The '''lumped-matter discipline''' is a set of imposed assumptions in [[electrical engineering]] that provides the foundation for '''lumped-circuit abstraction''' used in [[Network analysis (electrical circuits)|network analysis]].<ref>Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare ([http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/6002_l1.pdf PDF]), [[Massachusetts Institute of Technology]].</ref> The self-imposed constraints are:
# The change of the magnetic flux in time outside a conductor is zero. <math display="block">\frac{\partial \Phi_B} {\partial t} = 0</math>
# The change of the charge in time inside conducting elements is zero. <math display="block">\frac{\partial q} {\partial t} = 0</math>
# Signal timescales of interest are much larger than propagation delay of [[electromagnetic waves]] across the lumped element.

The first two assumptions result in [[Kirchhoff's circuit laws]] when applied to [[Maxwell's equations]] and are only applicable when the circuit is in [[steady state (electronics)|steady state]].  The third assumption is the basis of the lumped-element model used in [[Network analysis (electrical circuits)|network analysis]].  Less severe assumptions result in the [[distributed-element model]], while still not requiring the direct application of the full Maxwell equations.