# Three inductors in series , of increasing inductance

1. Jun 3, 2014

### B0b-A

three inductors in-series, of increasing inductance , say 1μH , 10μH and 100μH , wire-gauge constant and wire has some resistance which is constant per unit length.

Is it possible to make the middle inductor, (10uH), the hottest of the three by adjusting the frequency of the AC passing through this series circuit ? , [ i.e. via a resonant, "tuning" effect ].

or will the biggest inductor (100μH) always be the hottest of the three regardless of the frequency of the AC in this series circuit ?

2. Jun 3, 2014

### Staff: Mentor

Why do you want the inductors to get hot?

3. Jun 3, 2014

### skeptic2

The only thing that causes heat is the resistance of the coil. Even if all the inductors have the same wire gauge (ohms per meter) it doesn't necessarily mean that the inductance is proportional to the wire length. Inductance can also be affected by the diameter of the coil, the type of core, the current through the coil (higher currents can saturate the core reducing the inductance) and even how the coil is wound.

4. Jun 3, 2014

### B0b-A

The heating was an unintentional side-effect.

If the coils were in parallel that wouldn't be true : at high AC frequencies there would be less current through the larger inductor because of its larger inductive-reactance , [ like a "choke" ]. Less current means less ohmic heating.

However in the case I outlined the coils are in series, not parallel.

Last edited: Jun 4, 2014
5. Jun 4, 2014

### Staff: Mentor

Yes, you asked about a series combination, and that is what skeptic2 replied about. The only additional heating effects beyond what he mentioned are AC losses (from eddy currents and other effects).

Can you provide some context to your question? What are you trying to do?

Also, keep in mind that inductors in close proximity can also share flux, which alters their inductance...

6. Jun 4, 2014

### B0b-A

I was reviewing someone else's design for an experiment which had three coils in series with an alternating current , and the assumption was that any heating would be greatest on the largest inductor, (with the largest number of windings).

If the coils were in parallel that would not be the case : at high frequencies of AC the current to the largest inductor would be choked and any ohmic heating would be reduced because of the reduced current.

I wasn't certain that similar frequency-depended behaviour couldn't happen in a series arrangement , which is what prompted the question.

7. Jun 4, 2014

### Staff: Mentor

The total inductance limits the AC current (as you know). AC losses and wire resistance contribute to the heating in the series circuit. The amount of heating in each depends on how you wind the inductors, the size of the cores, the geometry of the cores, the core material, etc. If you only vary the number of turns to make the different inductances on identical cores, then yes, the largest inductor will heat the most.

In your example, though, you probably wouldn't use the same core to make the 3 inductors that vary in inductance by 2 orders of magnitude.

Quiz Question -- how does the inductance vary with the number of turns?

8. Jun 4, 2014

### B0b-A

(Number of turns)^2

Back to the original question ... What if stray-capacitance is added , (see attachment) ,
could that cause the middle coil to become the hottest at some resonant-frequency ?

#### Attached Files:

• ###### series coils, now with stray capacitance.png
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Last edited: Jun 5, 2014
9. Jun 5, 2014

### Staff: Mentor

10. Jun 5, 2014

### meBigGuy

If C2 is a tiny capacitor and C1 and C3 are large capacitors the the currents through the inductors would not be equal.

On the other hand, Assuming the capacitors are reasonable parasitic values, Power factor will cause some variation, won't it? Any AC guy care to work that out?

11. Jun 5, 2014

### Staff: Mentor

The keyword for me was parasitic. IMO, the parasitic capacitances won't change the situation.

12. Jun 6, 2014

### Staff: Mentor

But the mutual inductances would change the situation if the inductors were stacked end-to-end.

Quiz Question -- if the inductor slugs were stacked end-to-end, how would that change the heating situation?

13. Jun 7, 2014

### meBigGuy

RE Quiz: are all the windings in the same direction?