How to Reason in Circuit Analysis

The following conversation played out in my head as I was grading an exam problem that had a supernode composed of two neighboring supernodes. Many students (in introductory circuit analysis) had difficulties with this problem, so here’s what I plan to present when I explain it.

HOW TO REASON IN NODAL ANALYSIS

Q: What is the main type of equation involved in performing nodal analysis?

A: KCL equation

Q: What electrical quantity is represented in each term of a KCL equation.

A: current

Q: Are there any elements for which, if the current is not stated, we do not have a way (a defining equation[1]) to know and express the current?

A: yes

Q: What are these elements?

A: voltage sources of any type[2] that are directly between two non-reference essential nodes (NRENs)

Q: Why is that a problem?

A: There is no defining equation (like Ohm’s Law) for a source, and if it’s directly between two NRENs, then there is no other element in series with it.

Q: So what if there is no other element in series with it?

A: If there were a resistor in series with it, we could use Ohm’s Law on the resistor.

Q: Why not use Ohm’s Law on the source?

A: Ohm’s Law does not apply to sources, does not deal with sources; it’s only for resistors[3].

Q: Fine… What’s with the non-reference thing?

A: If a voltage source (of any kind) has one terminal attached to the reference node (ground), then we automatically know the voltage at the other end (with respect to ground).

 

Conclusion: If there is a voltage source between two NRENs, circle it to make a (super)node, and write KCL out of that node, without going inside it (until later, when you need another equation, at which point you use KVL).

 

[1] A defining equation is an expression that relates current through a two-terminal element to the voltage across a two-terminal element by means of the inertial aspect of the element (its capacitance, resistance, inductance, and I suppose, pretty soon, its memristance) and the passive sign convention (PSC).

[2] i.e., independent voltage source, current-dependent voltage source, voltage-dependent voltage source: It’s about the voltage aspect, not about the dependence aspect.

[3] two terminal elements with a linear current–voltage relationship; note the en dash : )

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