I'm currently studying the textbook Fundamentals of Electric Circuits, 7th edition, by Charles Alexander and Matthew Sadiku. Chapter 2.4 Kirchhoff's Laws gives the following example:
Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero.
A simple application of KCL is combining current sources in parallel. The combined current is the algebraic sum of the current supplied by the individual sources. For example, the current sources shown in Fig. 2.18(a) can be combined as in Fig. 2.18(b). The combined or equivalent current source can be found by applying KCL to node \$a\$. $$I_T = I_1 - I_2 + I_3$$ A circuit cannot contain two different currents, \$I_1\$ and \$I_2\$, in series, unless \$I_1 = I_2\$; otherwise KCL will be violated.
I don't understand why a circuit cannot contain two different currents in series, and why this would violate Kirchhoff's current law. If two currents, such as \$I_1\$ and \$I_2\$, are in series, then wouldn't the current just be the net of the two, as shown in 2.18(b)? I get the impression that I am misunderstanding/misinterpreting what this is saying.
For some reason, despite the fact that we've had four answers, no one has yet explained this concept. The closest we've come is Neil_UK, who just commented that my reasoning is incorrect since I am assuming that the currents also add in series, just as they do in parallel. So why exactly is it incorrect to assume that the currents add in series, just as they do in parallel? This seems like it would be the natural assumption. What is the correct way to think about this?
From the same textbook, “a branch represents a single element such as a voltage source or a resistor.” And, again, from the same textbook, “a node is the point of connection between two or more branches.”