AC Circuit Theory Maximum Power Transfer

serpico4321 · Feb 23, 2013

Hello All,

I am currently hitting a barrier with regards to the basics of this question. It is for a HND so I may have put this in entirely the wrong forum. Apologies if so.

A 50HZ supply is connected to various given impedance's connected in series and parallel. Calculate the value of the load impedance and the maximum power transfer.

Maximum power transfer I understand is basically the Thevenin/Norton equivalent of Rth. But to acquire Rth surely you nee two values of ohms law?

Though THERE IS NO EMF indicated in the question. Is it possible to simply use the frequency given 50Hz and the impedances to calculate the maximum power?

Any help in the right direction would be vastly appreciated

Chr!s · Feb 26, 2013

serpico4321 said:
Thanks, Archy. Got that bit, using the modulus of impedance then combining resistors in parallel and in series, came up with 332.53 ohms.

Though to calculate the power transferred is P=I^2xR so would I not need another value? The supply says 50Hz not 50V

It's just asking for a load resistance which will achieve mpt

serpico4321 · Feb 26, 2013

Archy, Thanks for giving it a go, once i'm done with it believe me, I don't want to look at it for a long time! what value did you get out of interest?

Chr!s, The thevenin equivalent is no problem, but i'm assuming the question is asking for a value of the power transferred to the load in watts?

Do you think it is just asking for the load impedance only which will have to be equal to the circuits internal impedance for maximum power transfer? (as you say Rs=Rl). I hope so!

Chr!s · Feb 26, 2013

serpico4321 said:
Archy, Thanks for giving it a go, once i'm done with it believe me, I don't want to look at it for a long time! what value did you get out of interest?

Chr!s, The thevenin equivalent is no problem, but i'm assuming the question is asking for a value of the power transferred to the load in watts?

Do you think it is just asking for the load impedance only which will have to be equal to the circuits internal impedance for maximum power transfer? (as you say Rs=Rl). I hope so!

Yes load impedance only, it won't matter what the emf is, you have matched the two impedances so Rs=Rl

serpico4321 · Feb 26, 2013

Nice one, It's starting to get clearer, alas, there's still some fog!

Determine the value of the load impedance that will dissipate the maximum power (Thevenin impedance equivalent of the circuit) DONE

And the value of this power? (Do you reckon its just the way its worded?)

Chr!s · Feb 26, 2013

serpico4321 said:
Nice one, It's starting to get clearer, alas, there's still some fog!

Determine the value of the load impedance that will dissipate the maximum power (Thevenin impedance equivalent of the circuit) DONE

And the value of this power? (Do you reckon its just the way its worded?)

Well if Rs = Rl then the power dissipated in the load will be 50% of the total power dissipated in the circuit.

serpico4321 · Feb 26, 2013

Fantastic!

Chr!s, thank you. I've been looking at how to get power as watts which will never work without the correct values. Never though of it as a percentage, which by definition is a value.

I've just sent you up to 100 thanks as well. Appreciate your time.

Chr!s · Feb 26, 2013

serpico4321 said:
Fantastic!

Chr!s, thank you. I've been looking at how to get power as watts which will never work without the correct values. Never though of it as a percentage, which by definition is a value.

I've just sent you up to 100 thanks as well. Appreciate your time.

Your welcome. Good luck!

grantr37 · Feb 28, 2013

serpico4321 said:
Thanks for the replies! I'm looking to get the maximum power transfer for the load impedance. View attachment 17445 To calculate the power surely requires either current or voltage to which I am only given the 50Hz supply and the calculated impedance. I've attached a drawing (yeah I know!) Chr!s, 'There are two methods, the trial and error to plot from 0 - 3 ohms, or the first derivative method' I've not heard of the trial and error plot, is there any chance (please!) you could elaborate on this. Using either of these applications you can find the maximum power from only Frequency & Impedance? Thanks

did this on microsoft paint from scratch, please excuse as was done at 2:30 Am as I was up :rolleyes2:

grantr37 · Feb 28, 2013

will try to do some more bits and pieces for you on here when I can get the time :stuart:

Silly Sausage · Feb 28, 2013

grant,
There's an error in your solution.
The inductor is reactive so you can't just add it to the resistances.

X[SUB]L[/SUB] = j219.9

so Z[SUB]Th[/SUB] = 330.3 + j219.9

and Z=sqrt(R[SUP]2[/SUP] + X[SUP]2[/SUP])

Blame it on it being 2:30am!

Good drawing btw.