To find the maximum power that can be delivered to resistor that is specified

I have to find out the maximum power delivered to a load which is already specified.

It would not have been a problem if the load was not specified. In that case, I could have used Thevenin‘s theorem and Rth would have been the load resistance for maximum power transfer.

But here internal losses is to be adjusted in order to deliver maximum power to the 3K ohm resistor. So, how can I solve the problem?

• Apply KCL, perhaps...
– Chu
Jun 2, 2019 at 10:28
• By applying kcl my answer will not be achieved. Because i have to find out the value of R for which maximum power can be supplied to 3K ohm resistor. Jun 2, 2019 at 10:42
• You can find the maximum power in the 3k once you've determined $\small I_x$. $\small I_x$ is not a function of R or the 3k.
– Chu
Jun 2, 2019 at 14:05
• Okay I got this. Jun 2, 2019 at 15:07

You should write equations to find the $$\R_{TH}\$$ for everything to the left of the 3k resistor. You will find that $$\R_{TH}\$$ is a function of the unknown resistor value $$\R\$$. Now, find the value of $$\R\$$ that gives you the value of $$\R_{TH}\$$ that results in the maximum power transfer to the 3k resistor.
Apply KCL to the $$\\small 16\:V / 10I_x / 4\:mA\$$ junction; that gives the value of $$\\small I_x\$$, and then it's easy to find the value of $$\\small R\$$.