# Triac Dimmer Supplying a Purely Inductive load

I was asked a question in my lab viva today, on a triac switch supplying a fixed value inductor of 0.2 henry. How will the current and voltage of the inductor vary, if the triac's firing angle was varied between 90 to 120 degrees? Explain the nature of inductors voltage under different firing angles.

$$V_{load}=V_{peak} \cdot \sqrt{\frac{2\pi-2\phi+\sin 2\phi}{4\pi}}$$

which I derived there only and the inductor current will be out of the phase lagging by 90 degrees to voltage.

Vpeak is the peak voltage of the ac mains supply and $$\\phi\$$ is the firing angle of the triac.

Apparently, this wasn't the correct answer maybe.

So, what might be the correct answer to this or perhaps the correct generalized way to answer this question?

• Welcome to EE.SE! This appears to be a homework question. As such, you need to show us your work so far, and explain which part of the question you're having trouble with. For future reference: Homework questions on EE.SE enjoy/suffer a special treatment. We don't provide complete answers, we only provide hints or Socratic questions, and only when you have demonstrated sufficient effort of your own. Otherwise, we would be doing you a disservice, and getting swamped by homework questions at the same time. See also here. Sep 27, 2018 at 12:28
• I am sorry sir, but you really can't just shoot off accusing every question being a homework question. Sep 27, 2018 at 12:58
• I apologize for the confusion. When we say "homework" here, we don't necessarily mean literal homework, but rather any sort of "learning opportunity" that's intended to make you think. Did you not find any of the hints in my answer useful? Sep 27, 2018 at 15:35

The key is that the current starts at zero and goes as the integral of the voltage WRT time over the interval starting at alpha, ending when this integral is again zero.

Considering the integral as being the area under the curve, we can see that, ignoring diode drops and series resistances, for a sine wave conduction will be the area from alpha to 2Pi - alpha by symmetry.

For alpha in 0 -> Pi, current is zero outside the interval (alpha to 2Pi - alpha). While the RMS voltage or current is easy to evaluate given this, it is not particularly interesting, far more fun to evaluate how the current varies moment to moment while the thyristor is conducting, which is of course the integral of the applied voltage during conduction.

There will also at some angles be an unpleasantly high dV/dt which can be an issue for triacs in real systems.

Not even close.

The triac is a nonlinear, non-time-invariant device, which means you need to consider separately what happens when it is conducting and when it is not conducting, as well as exactly when it switches from nonconducting to conducting and vice-versa.

The key thing to keep in mind is that the triac turns on when the trigger occurs, but it turns off when the current through it drops to zero. The fact that the inductor modifies the phase relationship between voltage and current is VERY significant.

You may find that for some range of trigger phase angles, you get one kind of general behavior from the circuit, while for another range of angles, you get a very different behavior.

Your formula is actually a load RMS voltage vs. triac firing angle for resistive load vs. mains peak volatge.

There is nothing useful in finding voltage relation for inductor. The triac can't operate with arbitrary angle (0-180) for inductive load. You would need a current and voltage feedback to properly turn on the triac. These are so called phase angle controllers, for example motor speed controller. The firing angle looses its meaning, it is increased or decreased depending on motor speed.

Makes no sense to derive formulas, if at certain angles is totally impredictible, it would conduct on every second period, maybe,...

• What, I meant by 0 to 180 degrees is, what can be a generalized trend in change of voltage waveforms if the firing angle was varied in discrete steps between 0 to 180. Say it was varied as 0, then 30, 45, 60, 90, 120, and so on. Then, what might be the voltage waveform shape across the inductor at that particular alpha and perhaps will there be some general trend in the voltage waveform as alpha is increased or decreased in the given order Sep 27, 2018 at 14:04
• educypedia.karadimov.info/library/CD00003856.pdf , It's not so simple. At certain angle would fail to trigger. The difference makes also the initial conditions. st.com/resource/en/application_note/cd00003867.pdf . Practically you need a sort of algorithm or analog circuit, to drive an inductive load. Theoretically it's a wide field of study transients, nonlinear behaviour, saturation,...not an easy and neat answer what your tutor wants to hear from you. Perhaps he expects things that even he does not know, he made some oversimplification. Sep 27, 2018 at 18:38