Many circuits can be analyzed by progressively lumping and then unlumping elements while applying series and parallel formulas.

If you apply formulas and write down answers you are thinking like a technician (a respectable activity.) However, if you write down the formulas and then solve them all at once with algebra, you are thinking like an engineer.

Often a complex circuit is modeled as an equivalent circuit where many components have already been lumped.

An equivalent circuit is intended to solve one class of problems. It is important to ask, could there be something going on that is not captured by the model?

It is common to design circuits so that both its input and output can be though of as a 50 ohm resistors. Of course there is lots more going on but the 50 ohms is a useful fiction in that it enables much reasoning.

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Some circuits are immune to simple lumped analysis. Consider twelve equal resistors assembled into a cube with each resistor corresponding to an edge. Solve this by writing simultaneous equations. Those who paid attention in high school math will be rewarded.