Does placing two inductors in series make a current lag of 180 degrees?

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Discussion Overview

The discussion centers around the behavior of inductors in series and their effect on current phase relative to voltage, particularly in the context of transformer circuits. Participants explore the implications of connecting multiple inductors and the resulting phase shifts in AC circuits.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that inductors cause current to lag voltage by 90 degrees and questions whether two inductors in series would result in a 180-degree lag.
  • Another participant asserts that inductors in series combine to behave like a single inductor, maintaining a current lag of 90 degrees.
  • A participant reflects on their early misconceptions about electricity and acknowledges the complexity of understanding inductance and phase relationships.
  • One participant discusses the fundamental behavior of inductance, explaining that for a sine wave, the current always lags the voltage by 90 degrees, and emphasizes the importance of analyzing voltage phase shifts in circuits.
  • The same participant highlights that in complex circuits, various components can lead to different phase relationships, complicating the analysis beyond simple series or parallel combinations.
  • In the context of transformers, the participant clarifies that the inductance of windings is modeled as reactances, separating them from the resistive components in the analysis.

Areas of Agreement / Disagreement

Participants express differing views on the phase relationship of current and voltage with multiple inductors, with some asserting a consistent 90-degree lag while others question the implications of series connections. The discussion remains unresolved regarding the specific phase shift when combining inductors.

Contextual Notes

Participants reference the complexities of circuit analysis, including the effects of different components and the challenges in measuring current versus voltage phase relationships. There are indications of assumptions about ideal behavior that may not hold in practical scenarios.

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TL;DR
I understand that inductors make current lag voltage by 90 degrees. What if I connect two inductors in series? Would that make current lag by 180 degrees?
I understand that inductors make current lag voltage by 90 degrees. What if I connect two inductors in series? Would that make current lag by 180 degrees?
This question arose when I was studying the equivalent circuit of a transformer.
Screenshot 2025-04-25 185149.png


If Ip goes through Rc and Xm, does it mean that Xp would make Ip lag by 90 degrees and does that mean Xm would add 90 more degrees of lag in the current?
 
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Inductors in series sum, to make one inductor. That still only gives a current lag of 90°.
 
Interesting that having been involved with electricity and electronics since I was 8 years old or younger nowhere in my early years of self education did I wonder if that could be a thing. After a bit of book learning I guess I knew better than to question it. Believe me when I say I did have a great many misunderstandings early on. That's what happens when messing with electricity early in life. My parents likely worried I would burn the house down.
 
I think this question arose from the fundamental behaviour of inductance, v=L⋅di/dt, which for a sinewave, always has an exact 90° lag of current to voltage. The calculus of trigonometric functions decides that.

When we analyse circuits, we tend to look at and compare, the voltages on the different nodes, because we can measure voltage with a meter, or an oscilloscope, without breaking the circuit to insert an ammeter to measure the current.

We see varying phase shifts between the voltages on the nodes of the circuit, which are rarely exactly 90°. By changing the circuit components, we can use the circuit to build frequency dependent filters, or implement AC and DC coupling, that can make the circuits very useful for signal processing.

In complex circuits, it is voltage phase between nodes that we analyse. In those models, there are almost always, different R, L, or C, series and parallel components shown, that prevent a simple series or parallel combination of like components.

In the theoretical model transformer, presented by the OP, the virtual components have been separated as impedance components, Z=R+jX, as part of the analysis. Note that Np and Ns are the turn counts of the primary and secondary windings of the transformer, not inductors. The inductance of those windings is modelled separately, as reactances, jXp, and jXs.
 

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