Part I
Circuits at DC
The three laws are stated and exercised on resistive networks: Kirchhoff's current law, Kirchhoff's voltage law, and the element law, all carried out in real numbers. Every later part reuses this machinery unchanged.
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Lecture 1
Voltage, Current, Power, and the Sign Convention
A reference polarity and a reference direction are chosen before the answer is known, and neither can be chosen wrongly: an assumption that disagrees with the physics is reported by a negative number rather than by an error. Fixing the two references relative to each other is what allows a single product to report absorbed power throughout a circuit, and therefore what makes the powers of a whole circuit sum to zero.
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Lecture 2
KCL, the Branch-Current Method, and Equivalence
Kirchhoff's current law states that charge does not accumulate, at a single node or inside any closed surface drawn around several of them. From that one statement follows a systematic method that solves any resistive network, together with a set of equivalences by which the network is shrunk before the method is applied.
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Lecture 3
Nodal Analysis and the Supernode
Taking the node voltages as the unknowns costs one KCL equation per node, which normally yields a smaller system than the branch-current method requires. A voltage source between two nodes carries no current expression of its own, and is absorbed by drawing the KCL surface around both of its terminals.
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Lecture 4
Linearity, Superposition, and the Source Equivalents
Linearity has two consequences that govern the remainder of the course. Sources may be applied one at a time and their separate effects added, and any linear network, viewed from two terminals, is indistinguishable from a single source behind a single resistance.
Acknowledgment
The author thanks Jennifer Marley and Elena Veety for their help with the preparation of the course.