# 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
130
0

Sketched line of a generator is represented by the function approximation

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
421
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
16,892
5,202
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
130
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
16,892
5,202

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 $I$

$\frac{dP}{dI} =$

6. ### MrAl AAC Fanatic!

Jun 17, 2014
5,189
1,121
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
22,990
6,884
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.