Note: I do not need help in solving the question. I only need to understand the concept behind it.

In the thumbnail image below, a potentiometer is shown. My lecturer gave this as an example question. Subsequently, the resistance of Rth and R across load were evaluated in terms of x.

The lecturer subsequently used differentation to find the maximum power across the load.

Here is my question:

Why can't Rth = R across load be used to deduce maximum power across R load?
Why must differentation be used?

 

If we have a non linear graph we can use differentiation to locate the local maximum and minimum points, right?

If you plot the graph of power transfer when changing Rload and use differentiation to find the local maximum point on this graph then you find that to have maximum power transfer to the load the load resistance must equal the internal resistance of the source.

 

I understand what you mean but when I use R load = R th to evaluate the equation, the value of x and the value P max that I get is totally different when a differentiation method is employed.

 

1,of couse,u can use Rth = R across load to deduce max maximum power across the load,but most improtant u must add a equation there :R+Rth=10K.
2, u don't have to use differentation.just for simplicity.

 

I would think that provided you are permitted to invoke the Maximum Power Transfer Theorem as described in the AAC ebook then you would be able to apply it and simply work with Rth = Rload.

If on the otherhand the purpose of the problem is to require you to compute the Maximum Power Transfer rule, it would then require you to undergo the full derivation as you have done.

What value did you end up getting for x with the method you used? Also what value of x did you obtain for x when using simply Rth = Rload?

hgmjr

 

hitmen,

.....I only need to understand the concept behind it.

You and I both. I sure don't see why the circuit has to be Thevinized, Nortonized, sliced, diced or calculated. It seems to me that if you maximize the voltage across the 2k resister, then you have maximized the power. The way to do that is to wind the pot down to x=0 so that the parallel resistance of the pot and the load is maximized. That makes the voltage the highest it can be across the load, and the least amount of current is shunted through the pot. Moving the wiper to any other position will cause the voltage source to output more current, but not enough current will get to the load resistor to incease its dissipation, because the pot will shunt the current away from the resistor.

Ratch

 

Your professor seems like the type that hides behind his math and doesn't have much practical reasoning skills. I see this a lot!

It isn't a bad thing to prove your point with math, that's actually a very good attribute to have. The problem occurs when the person cannot derive a model to solve, then lacks 'common-sense' to approximate a solution.

Steve

 

hitmen,



You and I both. I sure don't see why the circuit has to be Thevinized, Nortonized, sliced, diced or calculated. It seems to me that if you maximize the voltage across the 2k resister, then you have maximized the power. The way to do that is to wind the pot down to x=0 so that the parallel resistance of the pot and the load is maximized. That makes the voltage the highest it can be across the load, and the least amount of current is shunted through the pot. Moving the wiper to any other position will cause the voltage source to output more current, but not enough current will get to the load resistor to incease its dissipation, because the pot will shunt the current away from the resistor.

Ratch

It's good to know this old(er) ME figured it out the easy way, too! (I figured I'd practice on the problem before looking at any of the prior work, just to dust off my skills.) Not as obviously as you did, but I got to that same conclusion quickly after figuring the voltage across the 2k resistor was just the source minus the drop across the 5k, and the max. power was going to be when that voltage was max, meaning the least drop across the 5k, which happens when the current from the source is minimized. I did a little algebra before I got to the duh! part. Probably wouldn't have passed the professor's "proof" criteria, judging from his work.