Where did I go wrong while solving for R_L?

[PainterGuy]

Hi,

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: http://img215.imageshack.us/img215/7743/imgtb.jpg

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

 

[gneill]

Your loop 1 equation looks to be incorrect. I see -9I₁ rather than -7I₁.

 

[PainterGuy]

Thanks a lot, gneill. You are correct. I have made an error.

Regards,

 

[PainterGuy]

Hi again, gneill

Please help me!

1: I have also used nodal analysis to solve the problem. Please have a look here: http://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: http://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

 

[gneill]

Hi again, gneill

Please help me!

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

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

Looks good.

2: I have tried nortonized the circuit and tried to find I_N using I_sc. Please have a look here: http://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?

After you substituted for I₂ in the loop 1 equation, you went on to clear the 5 in the denominator by multiplying through by 5. Unfortunately, you overlooked multiplying the 9V on the RHS of the equation by 5 also.