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Once again same circuit and same voltage source / current source and resistances. However now I need to calculate the maximum power that is consumed by the RL. How do I do that, and most importantly when I don't have the value on the load resistor?

Here is the shematic of the previous problem I solved (Thévenin equivalent):

schematic

simulate this circuit – Schematic created using CircuitLab

And the new question is this one:

enter image description here

Note: I1 should be 2 mA.

And here is the link to the question I submitted before this one:

How do I calculate load resistance?

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  • \$\begingroup\$ I1 is not 2 mΩ (well not in this universe anyway) \$\endgroup\$
    – Andy aka
    Apr 1, 2020 at 14:19
  • \$\begingroup\$ Yes, you are correct. It's 2 mA. \$\endgroup\$
    – Vetenskap
    Apr 1, 2020 at 14:25
  • \$\begingroup\$ Please fix your question then. \$\endgroup\$
    – Andy aka
    Apr 1, 2020 at 14:26

1 Answer 1

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The power in the load resistor is: $$P_L= I^2R_L$$

$$I=\frac{V}{R_{th}+R_L}.$$

Therefore:

$$ P_L=(\frac{V}{R_{th}+R_L})^2R_L.$$

To obtain the maximum power, differentiate and assign zero to obtain maximum:

$$\frac{d P_L}{dR_L}=0 \text{ therefore } R_L=R_{th} ~~~~~~\text{(NB.)}$$

This gives $$P_{max} = \frac{V^2}{4\cdot R_{th}}.$$

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  • \$\begingroup\$ I think you've misread the question. \$\endgroup\$
    – Andy aka
    Apr 1, 2020 at 14:20
  • \$\begingroup\$ No, I have not, I just skipped the middle part that he should practice. \$\endgroup\$
    – skvery
    Apr 1, 2020 at 14:25
  • \$\begingroup\$ Once again, how can I calculate all of this when the RL is unknown? \$\endgroup\$
    – Vetenskap
    Apr 1, 2020 at 14:29
  • \$\begingroup\$ Follow the above step-by-step. \$\endgroup\$
    – skvery
    Apr 1, 2020 at 14:31
  • \$\begingroup\$ I'm sorry, but I can't figure out how I can solve the first step when I have 2 unknowns ( PL and RL) to begin with? \$\endgroup\$
    – Vetenskap
    Apr 1, 2020 at 14:51

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