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

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SUMMARY

Connecting two inductors in series does not result in a current lag of 180 degrees; instead, the current continues to lag the voltage by 90 degrees. This behavior is rooted in the fundamental properties of inductance, where the relationship is defined by v = L⋅di/dt. The discussion highlights that while inductors in series sum their inductance, the phase shift remains constant at 90 degrees. Additionally, the analysis of circuits often focuses on voltage phase shifts rather than current, which can vary based on circuit components.

PREREQUISITES
  • Understanding of inductance and its phase relationship with current and voltage
  • Familiarity with AC circuit analysis and impedance (Z = R + jX)
  • Knowledge of transformer theory, including primary and secondary windings
  • Basic calculus and trigonometric functions related to electrical engineering
NEXT STEPS
  • Study the principles of AC circuit analysis and phase relationships
  • Learn about transformer modeling and the significance of turn counts (Np and Ns)
  • Explore frequency-dependent filters and their applications in signal processing
  • Investigate the effects of combining resistors, inductors, and capacitors in complex circuits
USEFUL FOR

Electrical engineers, students studying circuit theory, and professionals involved in signal processing and transformer design will benefit from this discussion.

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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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