I seem to have missed the point

SamR said:

I thought I understood voltage dividers but Jacobi's Law has added a new dimension to it. What I am seeing is to get the maximum power from the divider I must do 2 things.

• Match the Load Resistance to the value of the upper total Resistance of the Voltage Divider.
• Use as low a resistance value as possible for the resistors of the Voltage Divider.

So it is a balancing act. First I need to know the load and then design the Voltage Divider to supply it with as low a resistor value as possible to maximize the power available to the load. That is the dimension I was missing thinking I just had to provide a suitable voltage.

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You first have to decide what it is you are trying to accomplish. Are you trying to establish a desired voltage across the load or are you trying to deliver the maximum power possible to the load? These are completely different objectives.

If you are trying to establish a desired voltage across the load (or at a particular tap), then you want the values of the resistors in the divider to be much smaller than the load resistance. The greater the ratio, the better the voltage regulation. But it also means that you are dumping the vast majority of your power in the divider resistors.

If you are trying to get as much power to the load as possible and if you have control over the voltage divider resistors, then just remove them entirely and connect the load directly to the source. If you also have control over the load resistance, then make it equal to the internal resistance of the source.