Yes checking is good and lisa, you have had the valuable input of several different persons thoughts.

But I hope the really good thing is that you did the donkey work calcualtions yourself and can carry that forward and hopefully also are now much more comfortable with Thevenin.

With that comfort comes the ability to employ some short cuts, like Nandu.
But you should always be able to work through the rote solution in case the quick fix fails.

go well

 

Hi Al,

I totally agree with you about cross-checking with different variables to confirm that the solution is indeed correct.

As far as the current problem is concerned, it's best to tackle the actual circuit rather than the equivalent one and avoid the burden of lengthy calculations and associated errors.

Here's the final circuit diagram based on the stated conditions.

The reactances cancel out (the series-resonance pair is a short circuit and the parallel one an open).

The result - Maximum power transferred to the 4Ω resistive load = 16W.

Regards,

Nandu.

Hi there Nandu,

I think it was good of you to show your circuit and the load that complies with the problem requirements, and that you solved it knowing that the reactive parts would cancel out leaving just the real parts to deal with, and it takes little calculation effort. That's a good point.

As i am sure you know, because the load is complex and a complex quantity has just two parts where the imaginary part is either positive or negative (it cant be both) that means it can be simplified down to just one resistance and one inductance or capacitance. So going through the calculations shows us the values we can use for the resistance and either the inductance and capacitance, and we know which one to use based on the sign of the imaginary part. Without the calculations we would not know how to reduce the load to just two components rather than three. So in this case we could produce a load which has just one resistor and one inductor if we wanted to, but it would take the calculations to get us there.

 

In this problem the bare conditions only of the maximum power theorem were given so Lisa has not yet studied this theorem in full.

Mr Al
There are versions of the theorem that can shorten the 'full' calculations.

It is always a toss up whether to work from first principles or collect a 'bag of ticks'.

Some compromise is necessary as there is a trick for nearly every situation and that could therefore result in a very large bag.