[SOLVED] Thevenin equivalent circuit

[KerimF]

Would you please write me your results of PL versus RL?
I got for RL=16, PL=0.49 W.

 

[husny540]

These are my values
PL RL
0.463 10 ohm
0.482 20 ohm
0.441 30 ohm
So after plotting the graph i got RL in correspond to the maximum power as 20 ohm and PL as 0.482. Is this correct or is there any other solution? Or am i also supposed to enter 16 ohm to the graph, then i get

PL RL
0.463 10 ohm
0.49 16 ohm
0.482 20 ohm
0.441 30 ohm
By this i get RL to the maximum p0wer as 16 ohm and PL as 0.49. am i correct?

 

[KerimF]

Since you cannot use the derivative of PL to find the answer which is RL = Rth = 16 Ohm, you have to plot PL for as many values of RL as possible to find out that indeed PL_max occurs when RL = 16 Ohm.

To be more sure, you can test the values close to 16 as below:

RL - PL
15.9 - 0.489995185
16.0 - 0.49
16.1 - 0.489995245

 

[husny540]

That is in addition to the 10,20,16,30 ohms i have to consider some more values for the x axis that is for the resistive values, and then calculate the power, and from the graph to find the RL to the maximum power eventhough we already know that RL=RTh=PL because the question expects us to find the value for RL by using the graph, am i right?

 

[KerimF]

Yes you are.

 

[husny540]

Thankyou. If i'm to prove te results using the maximum power transfer theorem, can you say whether my explanation is correct? This is my answer...The maximum power transfer theorem states that the power transferred from a supply source to a load is at its maximum when the resistance of the load is equal to the internal resistance or the thevenin resistance of the source. so according to the graph, the maximum power occurs at a value of 4.9W which occurs when the resistive load is 16 ohm which is equivalent to the thevenin resistance and thus this proves that the maximum power occurs when the RTh=Rl. Am i correct?

 

[KerimF]

Yes you are. Only later this result (RL=Rs for PL maximum) will be proven using the derivative of the PL(Rth) function.
Then in the AC study, the result will be expressed by the load and source impedances (or admittances)... ZL and Zs where Z = R + jX.
So if Zs = Rs +jXs and ZL=RL + jXL, PL is maximum when... we leave this for later

 

[husny540]

Is my above explanation enough or am i supposed to take whatever you also have said into consideration?

 

[KerimF]

Your previous answer should be correct.

You told me that you are supposed not to know any other method to prove it than by plotting the graph of PL in function of RL.

 

[husny540]

Yes that is what i told you and it is by using the graph i have proved the result as typed above in the post.Thanks a lot in helping me in this thevenin question and if i have any doubts i'll forward those to you