How do I calculate for which value of resistance R generators shows the biggest power?

Discussion in 'Homework Help' started by thexy, Mar 27, 2016.

  1. thexy

    Thread Starter Member

    Dec 13, 2015
    126
    0
    [​IMG]
    Sketched line of a generator is represented by the function approximation
    upload_2016-3-27_11-28-31.png
    How do I calculate for which value of resistance R generators shows the biggest power?
     
  2. dannyf

    Well-Known Member

    Sep 13, 2015
    2,196
    420
    Calculate power as a function of R and set its first order derivative to zero to find its max.
     
  3. MrChips

    Moderator

    Oct 2, 2009
    12,853
    3,527
    Calculate Power by multiplying U and I and plot Power vs I.
    Determine at what current and voltage the Power is maximum.
     
  4. thexy

    Thread Starter Member

    Dec 13, 2015
    126
    0
    P=UI
    U0*I/U=I-0,2I/24-0,8*I^2/24^2

    What should I do than?
     
  5. MrChips

    Moderator

    Oct 2, 2009
    12,853
    3,527
    You made a mistake in your equation.

    Your original function is of the form:

    \frac{U}{U_0} =

    Multiply both sides of the equation with U_0

    Now multiply by Ito give Power = U * I

    Then take the first derivative with respect to I

    \frac{dP}{dI} =
     
  6. MrAl

    Distinguished Member

    Jun 17, 2014
    2,678
    550
    Hi,

    I am guessing that those commas are there to represent decimals. So 0,2 is 0.2 right?
    Still have to get used to seeing that, if that is what it really is.

    Yes, for a function F(x) the critical points can be found by solving:
    dF(x)/dx=0

    Have fun :)
     
  7. WBahn

    Moderator

    Mar 31, 2012
    18,256
    4,941
    What you should do then is ask if the units work out.

    You want units of power.

    Does Uo*I/U have units of power?

    Each term of the right hand side needs to have units of power. Since you still can't be bothered to track your units, it is impossible to tell what the units are for most of the terms. But what about that first term, I ? Does it have units of power?

    Always, always, ALWAYS track your units and check them. Otherwise you will blithely go chasing rabbits down holes when you could and should have known from the early on that your work was guaranteed to produce the wrong answer.
     
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