Question
Consider a heating system with strongly inductive characteristic and with an electronic control of temperature performed by varying the firing angle of a single-phase controlled bridge.
a) Determine the value of resistance to to ensure a maximum power of 7500W if this system is powered with 220V (effective).
b) Determine the fire angle to a power of 3000W.

My attempt of solution:
a)
If the system is strongly inductive so the current is constant, then we should use average voltage. So, maximum power is when the average voltage is maximum and this is possible when fire angle = 0 degree. Then:

And the resistance is:

b) Using the same idea:

The problem is:

Many friends (and maybe the professor) solved this problem on a exam using 220 V as voltage to find the resistance when maximum power, but I don't think this is totally correct because the problem tells us that the system is strongly inductive, so Irms = Iaverage = I constant, then, to find the voltage we should use average voltage and not effective as many other did. So, What do you think ? If I'm incorrect, why ? I'm a bit upset because I studied a lot for this exam and I was confident that the correct was average voltage when constant current.

 

the problem tells us that the system is strongly inductive, so Irms = Iaverage = I constant, then, to find the voltage we should use average voltage and not effective as many other did.

I believe you are correct if the inductance is large enough that the current through the resistor is essentially DC, since the average current through an inductor is proportional to the average voltage, not the RMS voltage.

 

I believe you are correct if the inductance is large enough that the current through the resistor is essentially DC, since the average current through an inductor is proportional to the average voltage, not the RMS voltage.

Well, I really don't know, but "strongly inductive" for me is DC current.

Do you know if is possible to find a resistance that 7500 = 220²/R could be correct ?
What can I tell to my Professor if he doesn't accept my solution ?
Is there any book that have a similar exercise solved ?

 

Do you know if is possible to find a resistance that 7500 = 220²/R could be correct ?

Only if that full AC voltage is appearing directly across the resistance and that's not the case with a large inductor in series.

What can I tell to my Professor if he doesn't accept my solution ?

You will have to ask him for the proof of his solution.

Is there any book that have a similar exercise solved ?

I don't know of any, offhand.

 

Highly inductive means large phase difference to me........not DC.

 

Highly inductive means large phase difference to me........not DC.

Sorry, I don't understand. How to solve the problem this way ? I think strongly inductive is like a "big" inductor that works like a DC source of current.

 

Highly inductive means large phase difference to me........not DC.

The output is from a bridge, which is pulsed DC.

 

Pardon me.