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We all know the basic example of school with series and parallel resistors, so they might be a good place to start.

Given two terminals $A$ and $B$ from a circuit, if the current that exists $A$ is the same as the one that enters $B$, then $$R_{eqAB} = \left|\frac{V_A-V_B}{I}\right|$$.

But what if in the real circuit not all the current exiting $A$ enters $B$? How would we calculate the equivalent current of the equivalent resistance? (The $I$ on the formula I posted above).

An example is the classical solution to the equivalent resistance of infinite grinds, they seem to understand the concept of equivalent resistance a bit better than the average high schooler on those solutions. Here is a question which explains it a bit further. There are much more examples, but the classic series/parallel ones we're used to, won't do the trick.

BioPhysicist
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hellofriends
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Equivalent resistance is the value of a single resistance that would draw the exact same current from a battery or power supply attached in a specific location in a circuit. The equivalent resistance of course is going to depend on where you attach such a battery, but if you place a battery somewhere in a network of resistors such that current leaves it, the battery is going output some specific current, so we can get away with pretending a network of complex resistors drawing some specific current is acting like a single resistance whose value is $$R_{eq}=\frac{V_{battery}}{I_{battery}}$$ Where the subscripted $V$ and $I$ are the voltage across the terminals of and current directly leaving the battery that you have attached. It is impossible to define equivalent resistance unless you choose two locations in a circuit to determine the equivalent resistance between, but once you have and imagine placing a battery there, there is always going to be a well-defined current leaving the battery. You are correct that reduction of the circuit to an algorithm of series and parallel rules doesn't always work- in such situations we must rely on more clever tools of imagining how much current would leave a battery when placed there.

mike1994
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But what if in the real circuit not all the current exiting A enters B?

Kirchhoff's current law (KCL) tells you that if you only connect your source to terminals A and B, then any current the source pushes in to terminal A must come out of terminal B or vice versa.

This is because the source doesn't create, destroy, or store any charge. It only pulls charge out of the circuit at one terminal and delivers it to the circuit at the other terminal.

The Photon
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