I seem to have missed the point

Thread Starter

SamR

Joined Mar 19, 2019
5,024
An exercise from Floyd examining Resistance and Power. I gathered and plotted the data but somewhat confused as to just what the point here was. Power increased rapidly as resistance increased then it peaked and power appears to be decreasing linearly as the resistance continues to increase. The Voltage is a constant 12V and I would expect a linear slope for I/R. What is it that I am failing to see here.
Cap1.jpg
Cap2.JPG
 

Thread Starter

SamR

Joined Mar 19, 2019
5,024
~5k including the 2.7k fixed resistor. So 12V/5k = ~2.5mA... Nope still don't see it... To extrapolate, as R continues to increase I continues to decrease until P~=0...
 

danadak

Joined Mar 10, 2018
4,057
Your graph shows peak power occurs at ~ 2.5K, 2.6K. When the load R
= R1. An important design result.

So if you have an energy source with a known internal impedance and want
to transfer maximum power out of it the above result tells you what the load
has to look like. Very profound, and constraining, result in many designs.

Regards, Dana.
 

joeyd999

Joined Jun 6, 2011
5,220
~5k including the 2.7k fixed resistor. So 12V/5k = ~2.5mA... Nope still don't see it... To extrapolate, as R continues to increase I continues to decrease until P~=0...
Rephrase: At what R2 is maximum power dissipated by R2?

And how does that relate to R1?
 

WBahn

Joined Mar 31, 2012
29,932
An exercise from Floyd examining Resistance and Power. I gathered and plotted the data but somewhat confused as to just what the point here was. Power increased rapidly as resistance increased then it peaked and power appears to be decreasing linearly as the resistance continues to increase. The Voltage is a constant 12V and I would expect a linear slope for I/R. What is it that I am failing to see here.
At very low load resistances, the current through is a maximum but the power delivered to the load is very low. Can you explain why that is?

At very high load resistances, the voltage across the load is a maximum but the power delivered to the load is very low. Can you explain why that is?

So if we are trying to get as much power transferred from the source to the load as we can (by choosing the value of the load resistance) we can't do that by either maximizing the load current or the load voltage, instead the optimal value is some balance of the two.

Compare the value of the load resistance to the value of the fixed at the point were maximum power was delivered to the load and see if you notice anything.
 

Thread Starter

SamR

Joined Mar 19, 2019
5,024
What I can "see" is that at 0Ω current is ∞ and at ∞Ω current is 0. So as they approach crossing W is Max? And why does after Max the slope appear linear? I would think W would be parabolic? There is also the squaring of current from P=I(IR)... So thatcap3.jpg graph should be something like this. Where I is squared. I hate paint... Now I'm not sure about what Dana says about matching PS impedance but there is something more here than I'm seeing.
 

Thread Starter

SamR

Joined Mar 19, 2019
5,024
OK, Dana clued me in. I had to think back on coil/transformer impedance matching. I get it but am confused as to why Floyd would throw this at me when discussing basic Ohm's Law and Power. Kinda got the cart before the horse here. Arghhh no we are talking DC here not AC...
 

Thread Starter

SamR

Joined Mar 19, 2019
5,024
@crutschow Thanks for putting a name to it. I thought I had missed/forgot something from Grob so I went back and looked for both the Theorem and Jacobi's Law. They weren't there! Floyd does cover it but several chapters further in so it kinda threw me. Still looking into it but thanks for putting me in the right direction to all of you.
 

Thread Starter

SamR

Joined Mar 19, 2019
5,024
When R2=0, I is finite -- and a definite, computable value.
Indeed and I was referring at that point to Rtotal. And while the slope after Wmax appears linear it actually has a bit of a curve to it but otherwise pretty linear and I now understand why. I spent some time this morning reading up on Jacobi's Law and kinda surprised Grob never mentioned it. Apparently also going through the Floyd book is already yielding more insight into Electronics.
 

Thread Starter

SamR

Joined Mar 19, 2019
5,024
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.

IMG_0568[1].JPG.png
 
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