where did I go wrong while solving for R_L?

[PG1995]

Hi :-D

I was finding the value R_L for which maximum power takes place. Maximum power takes place when R_L = R_Th. Please have a look on the following link; you can see my answer is different: https://img215.imageshack.us/img215/7743/imgtb.jpg

Where did I go wrong? Please help me out. Many thanks.

 

[jony130]

You wrote for loop 1

-3*(2 I1) - 2 I1 - (I1 - I2) = 0 ---->> -6I1 - 3I1 + I2 = 0 ---->-7I1 + I2 = 0
-6 + -3 = ??

 

[PG1995]

Thank you very much, Jony. Yes, I do realize now that I have made an error.

I was trying to find R_Th using a current source but the answer is grossly wrong.
Have a look here: https://img19.imageshack.us/img19/5179/img0001naf.jpg

Please also let me know if my statement on KVL is correct for loop 2.

Regards
PG

EDIT: I made a blunder. I didn't shorted independent voltage source. Correct?

 

[_Eduardo_]

Why you are so orthodox to solve problems?
Why you like add unnecessary unknowns?

The voltage source can be placed after the R 4ohm and calculate the R Thevenin of that block. The final Rth will be Rth = Rth' + 4

In the right figure, just do:

Io = 1/2 + (1+3)/1 = 4.5A ==> Rth'= 1/4.5 = 0.222 .. ohms
​

Finally: Rl = Rth = Rth' + 4 = 4.222 ohms

 

[PG1995]

Thank you, Eduardo. Yes, you could find me a bit orthodox because I try to follow the procedure given in the book as closely as possible. You are very skilled in this stuff so many of the concepts would seem easier for you but they aren't for me! Gradually, I will also try to more 'liberal' while solving the problems. Thank you.

 

[jony130]

Well you forgot to short the 9V voltage source, and your answer is good.


But if we want to find Rth you need short the voltage source
And why you don't use the nodal? If you want to find the voltage the nodal is the best method becaues we already know the current 1A.



1A = V1/2 + (V1 - 3Vx)/1 (1)
Vx = (0 - V1)

1 = V1/2 + (V1 + 3V1)/1
1 = 9V1/2
1- 9V1/2 = 0
V1 = 2/9 = 0.222V

and Vo = V1 + 4Ω*1A = 4.222V

Rth = 4.222Ω

 

[PG1995]

Thank you, Jony.

1: I have also used nodal analysis to solve the problem. Please have a look here: https://img838.imageshack.us/img838/1970/prob1x.jpg

What is your answer to "Ref 1"? Is my answer correct?

2: I have tried nortonized the circuit and tried to find I_N using I_sc. Please have a look here: https://img39.imageshack.us/img39/3187/prob2s.jpg

My answer is not correct as you can see. The V_Th and R_th found previously in previous posts produce different value for I_N than the one found using I_sc. What did go wrong?

Please help me out. Many, many thanks.

Regards
PG

 

[jony130]

Thank you, Jony.

1: I have also used nodal analysis to solve the problem. Please have a look here: https://img838.imageshack.us/img838/1970/prob1x.jpg

What is your answer to "Ref 1"? Is my answer correct?

Yor answer to "Ref 1" looks correct

2: I have tried nortonized the circuit and tried to find I_N using I_sc. Please have a look here: https://img39.imageshack.us/img39/3187/prob2s.jpg

My answer is not correct as you can see. The V_Th and R_th found previously in previous posts produce different value for I_N than the one found using I_sc. What did go wrong?

Please help me out. Many, many thanks.

Regards
PG

Check you math, your equation looks good. and I see the error here

 

[PG1995]

Thanks a lot, Jony. It is very nice of you that you have helped me so much along with other members. I have a major test tomorrow. Let's see what happens.

Best wishes
PG