Can Adding Resistance to a Load Increase Maximum Power?

[Idea04]

I need some help to understand the maximum power theorom. From what I understand it states that in order to get maximum power from a source you have to match the resistance of the source to the resistance of the load. Now what i don't understand is how could adding resistance to a load generate more power. I thought electric power traveled a path to least resistance. And if the resistance of the source is high, let's say a kilo-ohm or mega-ohm, wouldn't the power from the source dissipate to nothing if it came across a load of such high resistance. Especially if the voltage from the source was low (lets ay under 3 volts).

 

[berkeman]

I need some help to understand the maximum power theorom. From what I understand it states that in order to get maximum power from a source you have to match the resistance of the source to the resistance of the load. Now what i don't understand is how could adding resistance to a load generate more power. I thought electric power traveled a path to least resistance. And if the resistance of the source is high, let's say a kilo-ohm or mega-ohm, wouldn't the power from the source dissipate to nothing if it came across a load of such high resistance. Especially if the voltage from the source was low (lets ay under 3 volts).

Classic problem -- good for you to understand it. *Given* some source Z (complex in the general case, not just resistive), if you load it with higher than that Z, you get a higher load voltage, but a lower load current. Calculate the result, and please show us your work.

And if you load the source with a lower Z, you get a higher load current, but a lower load voltage. Calculate the result, and please show us your work.

Now, use calculus (differentiate the right equation) to show what the best Zload is (again, complex) for maximum power transfer, given some pre-set source impedance. Please show us your work.