2nd Kirchhoff's law for all passive elements

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Discussion Overview

The discussion revolves around the application of Kirchhoff's 2nd law to circuits containing passive elements such as inductors, capacitors, and current sources. Participants explore the behavior of these components in relation to the law, particularly in the context of voltage summation around a loop.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about the behavior of inductors, capacitors, and current sources with respect to Kirchhoff's 2nd law.
  • Several participants assert that Kirchhoff's 2nd law applies to inductors and capacitors, stating the equation VI + VR + VL + VC = 0, emphasizing the time-dependent nature of voltages.
  • There is a suggestion that adding a voltage source in series modifies the equation to VI + VR + VL + VC = VV.
  • Another participant proposes rewriting the equation as VI + VR + VL + VC - VV = 0, questioning the orientation of the voltage source.
  • One participant expresses a preference for placing potential differences that favor current circulation on one side of the equation and those that oppose it on the other, describing this as intuitive.
  • A later reply advises marking diagrams consistently and summing voltages around loops, noting that unknown voltages may yield unexpected signs.

Areas of Agreement / Disagreement

Participants express differing views on the orientation of voltage sources and the interpretation of potential differences in relation to current circulation. The discussion remains unresolved with multiple competing perspectives on how to apply Kirchhoff's 2nd law in this context.

Contextual Notes

There are unresolved assumptions regarding the orientation of voltage sources and the definitions of potential differences in the context of current flow. The discussion does not reach a consensus on these points.

Jhenrique
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How would be the 2nd Kirchhoff's law for this circuit here:

attachment.php?attachmentid=70425&stc=1&d=1402186250.png


I'm asking because I don't know how is the behavior of the inductor, capacitor and current source wrt the 2nd Kirchhoff's law...
 

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Kirchhoff's 2nd law states that the sum of the voltages around a loop is zero. It also applies to inductors and capacitors so..

VI + VR + VL + VC = 0

The voltage (particularly on Inductors and capacitors) is time dependent but the above still applies at any instant in time.
 
CWatters said:
Kirchhoff's 2nd law states that the sum of the voltages around a loop is zero. It also applies to inductors and capacitors so..

VI + VR + VL + VC = 0

The voltage (particularly on Inductors and capacitors) is time dependent but the above still applies at any instant in time.

And if I add a voltage source in series in this circuit, the equation will be so:

VI + VR + VL + VC = VV

Yeah!?
 
Jhenrique said:
And if I add a voltage source in series in this circuit, the equation will be so:

VI + VR + VL + VC = VV

Yeah!?

Yeah!
 
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Yes. Although it might be better to write it as..

VI + VR + VL + VC - VV = 0

Did you realize you may have implied a different orientation for the additional voltage source VV?
 

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Last edited:
or if you prefer
 

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CWatters said:
Yes. Although it might be better to write it as..

VI + VR + VL + VC - VV = 0

Did you realize you may have implied a different orientation for the additional voltage source VV?

CWatters said:
or if you prefer

Interesting and confused!
 
But I don't think so... I place in the left side of the equation the potential difference that favors the circulation of the current and I place in the right side the potential differences opposes the circulation of the current. I can't think in another way more intuitive...
 
It's not always obvious if a "voltage" opposes or increases the current. Best practice is to mark your diagram in a consistent way, then go around each loop summing all the voltages. Then solve any simultaneous equations (eg for circuits with multiple loops). You may well find some unknown voltages turn out -ve when you were expecting them to be +ve.
 

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