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Homework Help: Find the resistance for maximum power transfer

  1. Oct 6, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the value of R where RL equals 50 Ω, for maximum power transfer
    I= 2A, R_L=50 ohms
    2. Relevant equations

    3. The attempt at a solution
    First, I created an open circuit including everything except R_L. Then i tried to solve for the Open Circuit Voltage,V_oc. Since current is only flowing through the left loop, it is safe to assume that I_x = the given current which is 2A. Therefore the voltage source =10V. The voltage on the bottom of the circuit will be 0, since it is grounded. I think the top voltage should be v1+10V. V1 would be i_x*40 which is 80. It is going in the opposite direction, so -80. That gives me V_oc=-70.
    Next I closed the circuit, still excluding R_L, and solved for the short circuit current with mesh analysis. I called the left loop i1 and the right loop i_sc. So it follows that
    solving for i_sc gives
    My teacher told us that the power transferred is at a max when R_thevenin=R_Load, so
    Solving for R I get R=-51.4 ohms, which is wrong...what am i doing wrong? Thank you!
  2. jcsd
  3. Oct 6, 2014 #2


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    Staff: Mentor

    Your problem occurred when you stated "V1 would be i_x*40 which is 80. It is going in the opposite direction, so -80." What did you mean by it going in the opposite direction? Opposite direction to what?
  4. Oct 6, 2014 #3


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    Homework Helper

    Better to solve the circuit with mesh analysis, and derive the expression for the output power and the input power as function of R.

    Last edited: Oct 6, 2014
  5. Oct 6, 2014 #4
    I thought that the current i_x was directed toward the ground, whereas the voltage i was looking for was at the top...so i guess that is were i got that from...i was reworking it, and i got i_x to be +80, which makes the problem have a nicer solution...didnt try it yet tho
  6. Oct 6, 2014 #5
    yeah i realized that wouldnt work, but a man can dream =]
  7. Oct 6, 2014 #6


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    Homework Helper

    I think the output power is on RL instead of R...
  8. Oct 6, 2014 #7
    yes, but we are already given R_L...i need to solve for R to maximize the output power on R_L
  9. Oct 6, 2014 #8
    OMG I GOT IT RIGHT! THE ANSWER WAS 5 OHMS....gneill was right, the problem was in the negative sign. Thanks! you guys are the best!!!!!!!!!
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