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

#### thexy

Joined Dec 13, 2015
130

#### dannyf

Joined Sep 13, 2015
2,197
Calculate power as a function of R and set its first order derivative to zero to find its max.

#### MrChips

Joined Oct 2, 2009
21,664
Calculate Power by multiplying U and I and plot Power vs I.
Determine at what current and voltage the Power is maximum.

#### thexy

Joined Dec 13, 2015
130
Calculate Power by multiplying U and I and plot Power vs I.
Determine at what current and voltage the Power is maximum.
P=UI
U0*I/U=I-0,2I/24-0,8*I^2/24^2

What should I do than?

#### MrChips

Joined Oct 2, 2009
21,664

Your original function is of the form:

$$\frac{U}{U_0} =$$

Multiply both sides of the equation with $$U_0$$

Now multiply by $$I$$to give $$Power = U * I$$

Then take the first derivative with respect to $$I$$

$$\frac{dP}{dI} =$$

#### MrAl

Joined Jun 17, 2014
7,757
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 #### WBahn

Joined Mar 31, 2012
26,064
P=UI
U0*I/U=I-0,2I/24-0,8*I^2/24^2

What should I do than?
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.