Timeline for Analyzing electric circuit with capacitor, inductor and resistor
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| May 15, 2022 at 0:59 | comment | added | Ján Lalinský | You can measure all potential drops on all elements in a real instantiation of this circuit, you just have to use quality meter and shielded probes, so that effect of the induced field near the inductor on the measurement is suppressed. | |
| May 15, 2022 at 0:52 | comment | added | Ján Lalinský | It is standard. Nobody can define potential based on total field, which has non-conservative component. The practice in electrical engineering of circuit analysis is that potential drop (sometimes called voltage or (oh no) voltage drop) on a perfect inductor is $LdI/dt$, and presence of induced non-conservative field near the inductor does not cause any problem to this statement. | |
| May 15, 2022 at 0:44 | comment | added | peek-a-boo | Well, another thing in your answer is that you seem to be using (atleast to me) a non-standard definition of potential (as that associated to 'the' conservative part). Here we have a non-conservative E-field, so I wouldn't even bother trying to come up with any definition for a potential. Anyway, this goes back to my comment about how we can always adjust our definitions and terminology to make two different analyses match up. There's obviously nothing wrong with that inherently, it's just that I find the Faraday/Maxwell approach infinitely clearer, hence I always use just that. | |
| May 15, 2022 at 0:39 | comment | added | Ján Lalinský | Exactly. I stressed this so that people realize these two methods seem to use different ideas, but in the final analysis they use the same assumptions and have the same results. | |
| May 15, 2022 at 0:37 | comment | added | peek-a-boo | My comment is merely intended to highlight that at the main level, I'm using Faraday's law to set up an ODE, and sure, if you want to be more specific, then I'm exploiting other facts to evaluate each of the path integrals $\int \vec{E}\cdot d\vec{l}$ across the various pieces in the circuit. | |
| May 15, 2022 at 0:36 | comment | added | peek-a-boo | @JánLalinský ok, you're right, I'm using more than just Faraday's law (though I did write down how I'm calculating things and where each contribution comes from in my 3rd paragraph without using specific names like Ohm's law etc). I mean there's a never ending rabbit hole of how deep down we want to give the explanation (e.g we can prove $e^{a+b}=e^ae^b$ by going all the way down to $\epsilon$-$\delta$ definition of limits, down to the field axioms for $\Bbb{R}$, and heck even down to the Dedekind cut definition of reals and even deeper down if we want); but that's besides the point. | |
| May 15, 2022 at 0:20 | comment | added | Ján Lalinský | @Stallmp the book is correct. Both the KVL method (very important in analysis of complicated circuits in electrical engineering) and the method here give the same result! | |
| May 15, 2022 at 0:17 | comment | added | Ján Lalinský | @peek-a-boo The KVL method is consistent with Faraday's law, because potential drop on inductor $LdI/dt$ that it uses is derived using Faraday's law. Also, "simply applying the Faraday law" is not all that your method does; the method starting with the Faraday law then needs to assume the generalized Ohm's law for resistor and null integral for inductor as well. In other words, both methods use the same assumptions and they are equivalent. | |
| May 14, 2022 at 10:36 | comment | added | peek-a-boo | having said this, I think sometimes people redefine their terminology about what exactly constitutes a voltage drop or emf so that their application of KVL is consistent with Faraday's law. However, I think playing with such linguistic matters is more confusing than simply applying Faraday's law (where the definitions are crystal clear and standard for what the $E$ and $B$-fields are), because like I said, all of classical E&M is based on Maxwell's equations. | |
| May 14, 2022 at 10:28 | vote | accept | Stallmp | ||
| May 14, 2022 at 10:28 | comment | added | Stallmp | Wow hahah I am actually blind, thanks! Thank you very much! So basically applying Faradays law gives the same result as in the book, but then the book says that the end result is because of KVL which is basically incorrect. Thanks for the recommendation as well, I will take a look at it! | |
| May 14, 2022 at 10:23 | comment | added | peek-a-boo | @Stallmp well the picture gives a battery/generator term right? The circle with the $E$? And yes, most of these books are wrong if they apply KVL. It's just not applicable here. IIRC Griffiths presents the LRC circuit the way I have written it down here using Faraday's law. Btw take a look at the lecture I linked to, it's explained very well in the first few minutes. When in doubt, ALWAYS stick to Maxwell's equations. They're literally what E&M is based on; you won't go wrong with them. | |
| May 14, 2022 at 10:18 | comment | added | Stallmp | Thanks for your comment! I am confused though, because there isn't a battery here right? There is only a conductor, resistor and an inductor, so where does the E(t) term come from exactly? Also is my statement correct that the book is incorrect by saying that KVL applies here? | |
| May 14, 2022 at 10:17 | history | edited | peek-a-boo | CC BY-SA 4.0 |
added 89 characters in body
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| May 14, 2022 at 10:12 | history | answered | peek-a-boo | CC BY-SA 4.0 |