Kirchoff's voltage law with coils

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Discussion Overview

The discussion revolves around the application of Kirchhoff's voltage law (KVL) in circuits that contain coils, particularly in the context of RL and RLC circuits. Participants explore the implications of changing magnetic fields and the assumptions underlying circuit theory.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants suggest that KVL may not apply to circuits with coils due to the need to account for external changing magnetic fields.
  • Others argue that KVL is applicable to RL and RLC circuits as long as the circuit itself is not treated as a coil.
  • One participant emphasizes that KVL and Kirchhoff's current law (KCL) rely on three assumptions: no net charge on components, instantaneous electrical effects, and no magnetic coupling between components.
  • Another participant points out that in RL and RLC circuits, while magnetic fields exist, they do not couple with other components, allowing KVL and KCL to remain valid.
  • Concerns are raised about path-dependence in voltage measurements, with some suggesting that different paths yield different voltage readings.
  • A participant mentions that the voltmeter creates another loop, which may affect the measurement depending on the magnetic field present within that loop.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of KVL in circuits with coils, with no consensus reached on whether KVL can be universally applied or if modifications are necessary in the presence of changing magnetic fields.

Contextual Notes

Limitations include the assumptions made about circuit behavior and the potential impact of magnetic fields on voltage measurements, which remain unresolved in the discussion.

bgq
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There is an idea that Kirchoff's voltage law could not be applied to circuit containing coils like this link.



What makes me confused is that almost all books apply Kirchoff's voltage law to RL and RLC circuit.
 
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bgq said:
There is an idea that Kirchoff's voltage law could not be applied to circuit containing coils like this link.
You have to modify the formulas to include external changing magnetic fields, here you just have to add 1V for going around the coil once (mainly at 5:55).

What makes me confused is that almost all books apply Kirchoff's voltage law to RL and RLC circuit.
Those circuits do not have external changing magnetic fields in them. Coils as part of a circuit are not an issue as long as the circuit itself (where you do your calculations) is not used as a coil.
 
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Thanks mfb, your comment are useful.

How can we find the value read by the voltmeter when connected to A and D measuring the voltage Va - Vd?
 
With Kirchhoff's laws, and counting the number of windings around the magnetic field.
 
This is a point which is sometimes not emphasized, but all of circuit theory requires three assumptions:

1) there is no net charge on any component
2) electrical effects happen instantaneously throughout the circuit
3) there is no magnetic coupling between components

When these three assumptions are met (or at least are reasonable approximations) then Maxwell's equations simplify to the KVL and KCL. When these assumptions are violated then KVL and KCL will be wrong.

In a RL or RLC circuit there are indeed magnetic fields within the inductor, but they do not couple to the other components, so the third assumption is still valid and KVL/KCL will work fine.
 
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mfb said:
With Kirchhoff's laws, and counting the number of windings around the magnetic field.

The problem here with Kirchhoff's laws is that this voltage depends on the path. We can say Vad = VR1 and we can say Vad = VR2, but each gives different results.
 
bgq said:
mfb said:
With Kirchhoff's laws, and counting the number of windings around the magnetic field.
The problem here with Kirchhoff's laws is that this voltage depends on the path. We can say Vad = VR1 and we can say Vad = VR2, but each gives different results.
Don't forget the second part in the quote:
and counting the number of windings around the magnetic field.
This takes the path-dependence into account.
 
mfb said:
Don't forget the second part in the quote:

This takes the path-dependence into account.

It is a single circuit, so there is only one loop, I can't see how this takes the path into considerations. Any formulas?
 
It is a single circuit, so there is only one loop
Your voltmeter forms another loop, and it is important if the magnetic field is inside this loop.
 

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