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Is there a difference between R-C and C-R circuit?

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When I connect 2 circuits A and B using serial RC circuit, is there a difference if I put cap first and resistor second or other way around? Can the black boxes A and B tell the difference? Are there some "gotchas"?

both are equal from the point of view of black boxes A and B.

There is no difference between either circuit until you tap a connection between the resistor and capacitor . In variant #1 , a tap between the resistor and capacitor would create a High pass filter . Variant #2 , with a tap between  capacitor and resistor , would create a Low pass filter .

You got the answer to the “if” question. Let me elaborate on how we know that.

Intuitive explanation:
There are only two variables that may be observed by a box: the current through that circuit and voltage drop on it.(1)

The current entering the resistor is always leaving it. The current entering the capacitor is always leaving it. So if the current can’t change in any of those components, it will always be the same no matter the order.

As for voltage, let’s first consider each component separately. The only thing each of them sees is the current and that determines the voltage across them. Since we know that the current is the same no matter where they are in this circuit, we can say the same holds for the voltage. And the voltage across the whole RC or CR pair is just a simple sum, which is insensitive to the order of summed elements.   

Simple explanation:
If you are just starting with electronics, it may be too early to introduce maths behind that. But it may be worth knowing such a concept exists. Resistors, capacitors and inductors may be described by a single number called impedance. That is a complex number that is resistance, capacitance and inductance at the same time. The impedance of a series of impedances is just a sum. And since sum is independent of the order in which we take elements, the impedance will be the same for both RC and CR arrangement.

(1) I did two mental shortcuts in here, but those are fine. First: there are two current variables, one for each wire going out of the box. But those are always equal in magnitude, so they may be considered one thing. Second: it’s actually voltage between the wires that is observed. But that depends directly on the voltage drop on that circuit — I just skipped that part to not make the explanation needlessly complicated and requiring unnecessary effort from me.

David Hess:
In theory there is no difference.  In practice there sometimes is because the parasitic elements to ground are different in the two configurations.

For example when a long wire is connected to the emitter or base of a transistor for the output or input signal, (1) a low value snubber resistor may be placed at the transistor to isolate the reactive component of the wire.  Moving this resistor to the other end of the wire would render it ineffective.

(1) Maybe the transistor is located remotely for better heat sinking, or it drives a long cable.


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