Internal resistance r.
Max power on R is
A battery has internal resistance
and open circuit terminal voltage
Show that the power supplied to a resistive load cannot exceed
well I only changed this to
but not sure how you determine what cannot be exceeded
mod.... this should of been put in "other topics" its not an advanced topic.
I've attached a circuit model of the situation. Would you agree with this model?
Let's say this model is accurate. Now what? Well, the one constant thing is the voltage of the battery. That doesn't change (at least, not theoretically). But as you change the load resistance, the relative voltage drops across each resistor changes. You want to maximize the power in the load. Now, Ohm's Law yields
The power dissipated in the load resistor is
Now use the usual Calc I procedure of setting
and solve for
What do you get?
sure appreciate the help... now I see how this works...thanks...
there was a follow up question on this.... not sure if input it right
thus if and .
Discrete loads of and are connected, one at a time, across the battery. Plot the curve of power supplied versus the ohmic value of the load. I tried to use the Wolfram|Alpha to graph this but didn't get the expression right http://www.wolframalpha.com/input/?i=plot[P%3D%28%2896%29^2%29%2F%284\Omega%29%3B%28P%2C-50%2C200%29%2C%28\Omega%2C-50%2C200%29]
Hence, verify that the maximum power transfer occurs when