EC-1.1 Node and Mesh Analysis
You can write and solve the node or mesh equations for any resistive network, and pick the method that leaves you with fewer unknowns before you start writing.
Two conservation laws generate every equation in this subject: charge does not pile up at a junction, and voltages around a closed loop sum to zero. Node analysis applies the first and mesh analysis the second, and the whole skill is choosing which one leaves less algebra and then being systematic about signs. The usual failure is not the mathematics but the bookkeeping, so the habit worth building early is labelling the reference and the assumed directions before writing a single equation.
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The two conservation laws, and what each one is really saying
Currents into a junction sum to zero because charge does not accumulate there, and voltages around a closed loop sum to zero because potential is single valued. Everything else in this subject is bookkeeping on top of those two statements.
NPTEL: Circuit Theory · CourseNode analysis: choose a reference, write one equation per unknown potential
Picking the reference node well removes an unknown for free, usually by grounding the node the most elements touch. Each remaining node contributes one equation, and the unknowns are potentials rather than currents.
NPTEL: Circuit Theory · CourseThe supernode: what to do when a voltage source sits between two unknown nodes
A voltage source between two unknown potentials fixes their difference but not either value, so the two nodes are treated as one region with a constraint equation beside it. This is the case most people get wrong first.
Mesh analysis: one current per window, and the sign convention that keeps it straight
Assigning a circulating current to each window of a planar circuit gives one equation per window from the loop law. Choosing the same rotation for every window makes the shared elements subtract rather than add, which is where sign errors come from.
MIT OpenCourseWare 6.002: Circuits and Electronics · CourseThe supermesh, and when a current source makes the loop law unusable
A current source shared between two windows fixes a current but leaves its voltage unknown, so the two windows are combined and the source supplies the missing equation. It is the mirror image of the supernode.
Count the unknowns both ways before choosing, and solve one circuit by each method
The same circuit is often three equations one way and six the other, and counting takes ten seconds. Solving one network twice and getting the same answer is also the cheapest way to find your own sign mistakes.
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