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Network analysis (electrical circuits)
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==Choice of method== Choice of method<ref name="ElectricCircuits">{{cite book |last1 = Nilsson | first1 = James W. | last2 = Riedel | first2 = Susan A. |title=Electric Circuits |publisher=Pearson Prentice Hall |year=2007 |isbn=978-0-13-198925-2 |edition=8th |url=https://books.google.com/books?id=sxmM8RFL99wC }}</ref>{{rp|pp=112β113}} is to some extent a matter of taste. If the network is particularly simple or only a specific current or voltage is required then ad-hoc application of some simple equivalent circuits may yield the answer without recourse to the more systematic methods. * [[Nodal analysis]]: The number of voltage variables, and hence simultaneous equations to solve, equals the number of nodes minus one. Every voltage source connected to the reference node reduces the number of unknowns and equations by one. * [[Mesh analysis]]: The number of current variables, and hence simultaneous equations to solve, equals the number of meshes. Every current source in a mesh reduces the number of unknowns by one. Mesh analysis can only be used with networks which can be drawn as a [[Planar graph|planar]] network, that is, with no crossing components.<ref name="ElectricCircuits"/>{{rp|p=94}} * [[Superposition theorem|Superposition]] is possibly the most conceptually simple method but rapidly leads to a large number of equations and messy impedance combinations as the network becomes larger. * [[Effective medium approximations]]: For a network consisting of a high density of random resistors, an exact solution for each individual element may be impractical or impossible. Instead, the effective resistance and current distribution properties can be modelled in terms of [[Graph (discrete mathematics)|graph]] measures and geometrical properties of networks.<ref>{{Cite journal|last1=Kumar|first1=Ankush|last2=Vidhyadhiraja|first2=N. S.| last3=Kulkarni|first3=G. U .|year=2017|title=Current distribution in conducting nanowire networks|journal=Journal of Applied Physics| volume=122|issue=4|pages=045101|doi=10.1063/1.4985792|bibcode=2017JAP...122d5101K}}</ref>
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