Inductance: Can L1 and L2 be replaced by an equivalent inductor in Figure 4(b)?

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Discussion Overview

The discussion centers around the possibility of replacing two inductors, L1 and L2, with an equivalent inductor, Leq, as depicted in Figure 4(b). The context involves exploring the mathematical relationships and conditions under which this replacement is valid, focusing on the implications of mutual inductance.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • One participant presents a mathematical expression for Leq and seeks validation on their approach, indicating they have been struggling with the problem.
  • Another participant references a previous thread that may provide additional insights into the topic of parallel mutual inductances.
  • There is a suggestion that a prior contributor, 'his_tonyness', may have correctly addressed part 'C' of the problem, based on the lack of corrections to their response.
  • A participant expresses gratitude for the assistance received, indicating a collaborative atmosphere.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the correctness of the proposed solution or the equivalence of the inductors, as participants are still exploring the problem and referencing past discussions.

Contextual Notes

Participants have not fully resolved the mathematical steps or assumptions necessary to validate the equivalence of L1 and L2 with Leq. The discussion reflects ongoing uncertainty regarding the application of mutual inductance in this context.

james123

Homework Statement



(c) See if you can show that L1 and L2 can be replaced by the

equivalent inductor, Leq, of FIGURE 4(b) where Leq = L1L2-M^2/L1+L2-2M

Homework Equations

The Attempt at a Solution


[/B]
I+I1+I2

Leq = V(L2-M)/jω(L1*L2-M^2) + V(L1-M)/jω(L1*L2-M^2)

= V*(L1+L2)-2M/jω(L1*L2-M^2)

V/jω*Leq = L1*L2-M^2/L1+L2-2M

Can anybody tell me if I'm close with this one or not? Struggling for days with it!

Any advice is appreciated!
 
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Ahh great! So after reading through I presume 'his_tonyness' got part 'C' correct since he wasn't corrected by yourself apart from I=I1+I2?
 
james123 said:
Ahh great! So after reading through I presume 'his_tonyness' got part 'C' correct since he wasn't corrected by yourself apart from I=I1+I2?
I believe that is the case. It's been a while since I took part in that thread (2015).
 
Many thanks gneill!
 

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