Sign of the terms in a circuit

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    Circuit Sign Terms
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Discussion Overview

The discussion revolves around the sign of the ##L\frac{dI}{dt}## term in the context of DC circuits. Participants explore the implications of different sign conventions in the formulation of circuit equations and their potential impact on the resulting differential equations.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion regarding the sign of the ##L\frac{dI}{dt}## term, noting discrepancies between a textbook and Wikipedia.
  • Another participant states that the correct differential equation is ## \mathcal{E}=L \frac{dI}{dt}+IR +\frac{Q}{C} ##, where ## I=\frac{dQ}{dt} ##, and discusses the interpretation of the inductor's voltage as either a source or a drop.
  • A subsequent post reiterates the differential equation and seeks clarification on the meaning of ##\mathcal{E}## as the sum of voltage sources in the circuit.
  • Further clarification is provided regarding the notation used for ##\mathcal{E}##.
  • Another participant suggests that understanding the signs is best achieved by revisiting the fundamental principles, specifically referencing Faraday's law and the right-hand rule, and shares links to lecture notes for additional context.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct sign for the ##L\frac{dI}{dt}## term, with differing interpretations presented. The discussion remains unresolved regarding which sign convention should be adopted.

Contextual Notes

Participants reference different sources and interpretations, indicating potential limitations in definitions and assumptions regarding the signs in circuit equations.

Silviu
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Hello! I am a bit confused about the sign of the ##L\frac{dI}{dt}## term in the circuits (DC circuits). In my book it is defined with a minus, on wikipedia it is defined with a plus and I am not sure which one should I use. I can pick any sign I want and the result will come out right regardless? Won't I risk to get a wrong ODE if I have a different sign for that term? Thank you!
 
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Yes. The correct differential equation is ## \mathcal{E}=L \frac{dI}{dt}+IR +\frac{Q}{C} ##, where ## I=\frac{dQ}{dt} ##. ## \\ ## The inductor can be considered to be a voltage source/EMF with voltage ##\mathcal{E}_{inductor}=-L \frac{dI}{dt} ##, which can be put on the left side of the differential equation. Alternatively, it can be considered an element with a voltage drop of ## L \frac{dI}{dt} ## just like a resistor has a voltage drop of ## IR ##. The voltage drop is positive when the current is increasing.
 
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Charles Link said:
Yes. The correct differential equation is ## \mathcal{E}=L \frac{dI}{dt}+IR +\frac{Q}{C} ##, where ## I=\frac{dQ}{dt} ##.
Thank you! So here ##\epsilon## is the sum of any voltage source in the circuit? Something like ##\epsilon = \sum_i V_i##
 
Yes. And I get the symbol with \mathcal{E} surrounded by the Latex parameters.## \\ ## And please see the last couple of sentences I added to post 2.
 
Well the signs you understand best when going back to the first principles the circuit equations derive from. For induction it's of course Faraday's law, and there (as with all things having to do with curls and rotation) the right-hand rule is your friend. Here are some notes from a lecture, I've given to Texan engineering students some time ago. Maybe they are of some use (although in my very bad handwriting ;-():

https://th.physik.uni-frankfurt.de/~hees/physics208/phys208-notes-III.pdf

The part on induction you starts on page 106. The course website with some more material is here:

https://th.physik.uni-frankfurt.de/~hees/physics208.html
 

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