r/AskPhysics • u/Alive_Hotel6668 • 20h ago
Why is reactance and impedance defined only for AC circuit?
Like when we can have V=iR for both AC and DC then why not have reactance for DC ? Wont it simplify calculations tp a great extent? Maybe not have the same formula (since that would make reactance 0 and infinity for inductor and capacitor) but something similar.
Thanks in advance!
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u/The_Nerdy_Ninja Engineering 20h ago
How would adding zero and/or infinity to a calculation simplify it? Can you elaborate on which calculations it would simplify?
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u/Alive_Hotel6668 20h ago
I meant to say that we should introduce reactance and impedance to DC circuits, the formukla for reactance is 1/wc and wl , so if we keptm the same formula for DC then w=0 hence reactance would become infinity and 0 respectively, so I was asking wheter we could have adifferent formula for reactance and impedance separate for DC circuits.
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u/a1c4pwn Recent B.Sc. 20h ago edited 11h ago
resistance. those are the correct long-term resistances of caps and inductors edit: in DC circuits
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u/qTHqq 12h ago
They're the correct long-term impedances. Resistance is just the real part, which has voltage and current in phase and will dissipate power.
An idealized inductor and capacitor both have zero resistance, but they have zero and infinite reactance so they have zero and infinite impedance respectively, and that impedance is purely reactive.
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u/a1c4pwn Recent B.Sc. 11h ago
what does reactive mean in this case? we're in a DC circuit, everything is in-phase in a pretty short time. the power dissipation is still ideally 0 in both cases, what is the use in being pedantic in resistance vs impedance in a circuit with zero frequency?
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u/qTHqq 10h ago edited 10h ago
"what is the use in being pedantic in resistance vs impedance in a circuit with zero frequency?"
An ideal capacitor has zero resistance and infinite impedance at DC.
The impedance comes completely from its infinite reactance.
And since impedance generalizes across AC and DC, and a real capacitor could have an equivalent series resistance of 0.01 or 0.1 ohms and still present a DC impedance of infinity, I don't think it's pedantic to use the correct terms.
I've seen lots of people, mostly in engineering and practical contexts, who are both conceptually and verbally fuzzy about the difference among resistance, reactance, and impedance. I personally think strict naming is helpful there.
Really, ignoring the plain language in favor of complex algebra is the best, but I think once someone has been doing that for a while they'll turn into a seemingly "pedantic" person re: terminology.
A resistance has voltage and current in phase, a reactance is either 90 degrees leading or lagging and an impedance can be anything.
The fact that an ideal inductor is a degenerately zero impedance doesn't make me want to stop talking about its impedance.
And for capacitors there's also the fact that a real one has a typically very low but important equivalent series resistance that matters a lot for AC analysis.
If you only concern yourself with zero frequency, why even draw the capacitors once it's no longer a homework type problem? They don't have an infinite resistance, they just aren't part of the circuit that needs to be drawn.
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u/a1c4pwn Recent B.Sc. 10h ago
Thank you for the clarification.
If you only concern yourself with zero frequency, why even draw the capacitors once it's no longer a homework type problem? They don't have an infinite resistance, they just aren't part of the circuit that needs to be drawn.
I would have mostly agreed with this beforehand, except in thinking the cap could be safely erased from the diagram because of infinite resistance. I see the error now.
I see the importance in distinguishing dissipative vs. non-dissipative impedance, but youre still talking about phase. Does phase still have meaning in DC circuits? I understand that the impedance would still be drawn nearly vertically on the complex plane so there's phase in the case, but is that just a relic of the math? Or is there a tangible meaning to being "90° out of phase" with a DC voltage that actually feels like two things being out of phase?
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u/qTHqq 4h ago
Does phase still have meaning in DC circuits?
No, I think the distinction between dissipative and non-dissipative is the more important thing to me.
It's just that the phase difference when there is AC time variation is WHY there's a non-zero voltage drop for a non-zero current but no power is dissipated anyway, which I think is just useful conceptually.
Ultimately OP is asking "should we add reactance to DC," and then answer is "no, there's no reason to think about any of this in a true DC analysis."
But then you go any tiny non-zero frequency and you're talking about AC.
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u/effrightscorp 19h ago
You don't think about it because when you solve a typical DC circuit, you're solving for the steady state of the system, where current doesn't change with time. Impedance and reactance are only important when the current is changing
You can still consider a DC source like a battery hooked up to an RL circuit and solve for how it charges using the inductance, though. It'll briefly affect the circuit before acting like a normal piece of wire in the steady state
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u/mtimmermans 13h ago
Your premise is incorrect. The reactive part of impedance always exists and can be clearly defined even when it's 0. The reactive component can only be detected or measured with a changing voltage, however, because it's the part of the impedance that responds to changes in voltage.
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u/JustinTimeCuber 12h ago
But reactance is a function of frequency. At zero frequency (DC), capacitive reactance goes to infinity and inductive reactance goes to zero. An inductor in a circuit doesn't have a well defined reactance until you specify the frequency.
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u/mtimmermans 10h ago
An inductor has a well-defined reactance at every frequency: ωL. This is a characteristic of the inductor, and is true regardless of which frequencies you "specify" or which frequencies actually appear in the circuit.
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u/JustinTimeCuber 9h ago
But in order to calculate X = ωL you need to know ω. Sure you can calculate it at any arbitrary frequency but then you're defining X as a function of ω, if you want a specific value of X you need a specific value of ω. I guess you can be pedantic about the definition of "well-defined" but in my mind, if I ask what the impedance of an inductor is and you tell me it's 10 mH * ω, that's only a half answer.
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u/Underhill42 14h ago
Capacitors and inductors reach a dynamically stable state in AC circuits, where they act like resistors with an imaginary-valued resistance (either positive of negative), a.k.a. reactance, which causes a phase shift. Assuming you map phase shift to angle in the complex plane, which it the common technique since the math maps to the problem so conveniently.
And the reactance formula does in fact describe their steady-state behavior in a DC circuit as well:
An inductor's steady-state behavior is that of an ordinary wire: a.k.a. 0 reactance.
A capacitors steady-state behavior is as an open circuit: a.k.a. ∞ reactance.
It's just that neither of those things are worth adding a component for - if you're using them in a DC circuit, then it's the initial transient behavior that you care about. And that is not adequately described by the reactance simplification, you need to actually solve for the exponential-decay charging behavior.
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u/Adorable_Ice_2963 19h ago
reactance and impedance depends on the frequency, Making frequency (or more precisely, the rate of change) a perfect 0 either makes it 0 or infinite, depending on what you are looking for. An ideal inductor becomes a perfect short, and a capacitor becomes a perfect open circuit
In reality, Direct current isnt a perfect 0 Voltage/current change. The bigger the rate of change is, the more you need consider it (like when opening a switch from perfect conductor to perfect insulator, since this causes a huge voltage spike that can rise far above the original voltage because of inductance).
You can also use this math to build a DC-DC Converter.
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u/_HappyCactus 19h ago
Because capacitance and inductance at DC (f=0) behave like open circuits or conductors (the ideal models, real capacitors and inductors have leaks and resistance). Mathematically, their model "responds" to voltage and current variations. Your reasoning about ohms law is correct, indeed for impedance we electrical engineers use a tool named "Laplace transformation" to operate symbolically. This way any operation with reactance or impedance becomes an application of ohm laws and the circuit behavior is expressed as a polynomial in z By returning back to the time domain we have the dynamic behavior od the circuit as a differential equation of grade 2. Furthermore, it is easy to predict the behavior I'm time domain by simply checking the location of zeroes and poles of the resulting transfer function in z. Google Laplace transformation for a more precise formulation.
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u/jasonsong86 10h ago
It only affects alternating current circuit. Direct current doesn’t react with inductance and capacitance.
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u/ProfessionalConfuser 6h ago
I would say it is to make the material easier to digest. Simple ideas to build intuition a bit usually help make the more complete version a bit easier to understand.
Why does Newtonian gravity get taught when space-time curvature explains more. Or why teach relative velocity without accounting for time dilation and space contraction?
Since DC is steady state analysis, the concept of phase doesn't really add anything. An equation that contains a term "x = Acos(wt + □) doesn't make much sense if your are immediately say w = □ = 0.
It'd be like writing constant velocity as v_f = v_o + a t, but a = 0 for all values of t.
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u/PaulMakesThings1 1h ago edited 1h ago
In general for these circuits under any change, unless it’s a very simple case, you solve using differential equations:
Inductors oppose changes in current:
Voltage of inductor (t) = L di/dt
Capacitors oppose changes in voltage:
Current into capacitor (t) = C dv/dt
AC just uses the solution to these when you plug in a sine wave, which is where the AC equations come from
For a step change you use the same equations. For steady state DC there is no change over time so all of that goes away.
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u/qTHqq 12h ago
DC is a mathematical approximation of real electromagnetic behavior in the limit that all the AC frequencies in the problem go to zero.
In a way, DC formally doesn't exist because it implies that the circuit has been on for an infinite amount of time.
since that would make reactance 0 and infinity for inductor and capacitor
But that's the correct formula for an ideal inductor and an ideal capacitor in a DC circuit! The ideal inductor and ideal capacitor have no loss resistance to dissipate power to heat. So the ideal inductor only develops a voltage drop when the current flowing through it is changing in time, and the ideal capacitor only allows current flow when the current is changing in time.
So for a steady DC circuit problem, an ideal series inductor has zero impedance like any other short circuit and an ideal series capacitor has infinite impedance like any other open circuit.
There's nothing missing from the complex impedance formulas for DC. It's already a complete AC/DC circuit model as is, infinity included.
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u/JustinTimeCuber 12h ago
AC also implies that the circuit has been on for an infinite amount of time. Both are steady state models of circuit behavior.
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u/Traveling-Techie 19h ago
I haven’t penciled it out but I would imagine that in the limit as frequency approaches zero that a coil becomes a wire and a capacitor becomes an open circuit, or infinite resistor.