Help finding maximum power transferred to load RL

This isn't homework, it's just a review problem. The answer is 4mW. I tried working the problem and came up with the wrong answer. What did I do wrong, and how can I solve this correctly?

My steps:

1. Remove $R_L$ and create an open in its place
2. Find the voltage at the open, this is the open circuit voltage
3. I applied KCL at node 2 (what I labeled V2)
• 6/3k amps in, 2mA out, 2mA in, and thus the current going out through the 6k ohm resistor (center branch) is 2mA. 2mA * 6kohms = 12 V across the 6kohm resistor.
• Also, there is 4V going across the 2kohm resistor.
• 12 + 4 = 16, so the open circuit voltage is 16V.
4. Opening the voltage source and shorting the current source, the internal resistance is 6k ohms (2k ohm is ignored, no current flow, and 3kohm is ignored, no current flow)
5. The Thevenin equivalent circuit has a 16V source, 6kohm internal resistance, and 6kohm load R_L. The voltage divides evenly. So, 8V/6kohms = 1.3mA through RL
6. P=IV, 1.3mA * 8V = 10.667 mW

What did I do wrong?

• Find the maximum power...as what parameter is varied? Jul 17, 2014 at 0:30
• I'm sorry, I do not understand what you are asking @PhilFrost
– asdf
Jul 17, 2014 at 0:31
• If we are finding a maximum, then it suggests we are trying to find the maximum of some function that has some parameters. What are the parameters? What do we vary to find the maximum? Jul 17, 2014 at 0:33
• Well, I know that maximum power is delivered when the internal resistance of the circuit is equivalent to the resistance of the load (or vice versa).
– asdf
Jul 17, 2014 at 0:37
• So we are asking what value of RL results in the maximum power in that load, and what will the power be under those conditions? You can't just ask "what's the maximum power in some load" if you don't specify what the load is. Maybe RL is 100M, and then the maximum power is very nearly 0. So is the minimum power. Jul 17, 2014 at 0:40