In most text books and other electronics material it's said current is flowing through the circuit. Isn't this wrong? As current is flow of charge. Is there anything such as flow of flow of charge?
"Flowing" qualifies state of flow
"Current is flowing" implies current not equal to 0.
It's semantically correct. Same as, "The river is flowing."
Websters, #2: River: A large quantity of a flowing substance
It describes the degree to which the flow is occurring (e.g. not zero).
The presumption of the question is wrong
"Current is flowing" does not equal "flow of flow of charge"...
...it equals "flow of charge is flowing."
At worse, it's redundant (not wrong). Typically it's just used as I described above (to indicate a non-zero quantity).
For non-English majors (like me!), here is more detail on this specific use case from english.SE.
Essential vs. temporary attribution
Here's a highlight from the English community (user Choster, a professional writer in Washington, DC):
We would identify something as a river because we ordinarily expect it to have the characteristics of a river, even if some of those characteristics are temporarily suspended. That is, a permanent or semi-permanent stream would be a river even if it has temporarily stopped streaming, as noted in the comments, by drying up, being dammed up, or being frozen solid.
On the other hand, something which only temporarily takes on the characteristics of a river could be called so, metaphorically, but only while it possesses those characteristics. If they cease, the metaphor is no longer applicable. If I spill a jar of molasses, I may report a river of molasses running down the table leg, but once the flow stops, we would lose the river (having gained a pool).
Current is a flow and flows may be interrupted, suspended, and resumed. A charge does not lose its ordinary expectation to flow just because it is momentarily not moving.
Flow is a rate
Electric current is the rate of movement, not strictly "electric charge in motion". Because this difference is subtle and has little impact on day-to-day design and analysis work, it's largely ignored (as it should be).
A quantity "charge in motion" would have units of yes/no -- is it "charge in motion" or not? To be more useful we need quantities that describe the motion.
That is why current is defined as the rate at which charge transits a normal surface. That is, current is the flow of charges, described by how much charge moves in unit time.
Perhaps it is more illustrative to see that "velocity" is not "meters in motion," even though velocity is describing the motion in units of meters (per unit time).
Another way to intuitively grasp this idea is to work backwards. In ordinary practice we readily except the idea of "zero as a number" and in engineering (especially appertaining current) doubly so -- "The current into the lightbulb is 0-Amps."
The reason current can be 0, as a quantity, is because it is describing a rate.
THE STUFF THAT FLOWS THROUGH WIRES IS CALLED 'ELECTRIC CURRENT'? Horribly misleading!
Most K-12 textbooks discuss a substance or energy called "current". They constantly talk about "flows of current." However, here's a pointed question: what flows in rivers? Is it water, or is it "current?" If I fill a bucket from the faucet, is my bucket full of "current?" No! Water moves, water flows in pipes, not "current." A flow of water is a correct phrase, while "a flow of current" is not. The same idea applies to electricity: electric current is a flow of a substance, but the name of the substance is not "current."
Since a current is a flow of charge, the common expression "flow of current" should be avoided, since literally it means "flow of flow of charge." --Modern College Physics: Sears, Wehr, & Zemanski
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Go check out his website -- he talks about several similar misconceptions.
Natural language cannot be read by macro-expansion of words with their definitions. You have to process language semantically, and not in a machine-like manner.
Flowing is what a flow does. A flow of charge flows through a circuit, hence a current flows. The charge flows also.
But if we ask what is the flow of, it is a flow of charge, not a flow of the flow of charge (even though the flow of charge flows). A flow does have a flow rate, however. What is the flow rate of that flow? is a grammatical question. We can elide the first flow in that sentence, but we can also elide rate: What is the flow of that flow? The first flow refers to the quantity, and second to the phenomenon.
Do you also suspect that it's wrong to say that a river flows, because it is actually water that flows whereas the river stays where it is? The idea of such a semantic restriction runs contrary to numerous human languages from all over the globe.
I don't see anything wrong with it. Can we talk about wind blowing or a gust of wind? Wind is, by definition, a flow of air. Wind is the word we use for air when what we care about is the air's movement, and not really the air. Yet, we wouldn't complain about gusts of wind, would we? If gusts of wind are valid, what's wrong with flows of current?
Even when there is no electromotive force, the current flow is still defined. It is zero, which is different than saying it doesn't exist, or is otherwise invalid. On a stagnant day, wind doesn't become air. The wind is still there. It is zero. Nor on a windy day does the air does become wind.
It would make sense that electrical engineers would favor current over charge, because charge that isn't moving generally doesn't do anything useful to the electrical engineer, as air that isn't moving can't do anything useful to the windmill operator.
According to dictionary.com, "flowing" is an adjective and, in this context, is defined thus:
moving in or as in a stream: flowing water.
Thus, "flowing charge" or "charge is flowing" means charge (is) moving in or as in a stream.
Now, charge moving in or as in a stream is precisely what we think of as "electric current" in a circuit context.
Then, "flowing current" or "current is flowing" is, literally, charge moving in or as in a stream is moving in or as in a stream.
Thus, if "current is flowing" means something else, then either "current" or "flowing" is being used in a different sense.
DrFriedParts proposes in his answer that "current is flowing" equals "flow of charge is flowing" and that this describes the degree to which the flow is occurring (e.g. not zero).
There is, in fact, a sense in which "flowing" describes degree:
abounding; having in excess: a land flowing with milk and honey.
So, it seems, "current is flowing" isn't redundant if "flowing" is used in this or a similar sense. Although flow of charge is abounding isn't precisely the same as flow of charge is non-zero, it's certainly in the ballpark.