- #1

jaumzaum

- 434

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- Homework Statement
- See below

- Relevant Equations
- See below

This was an exercise from the 2011 admission test of an university from Brazil:

40 identical generators with electromotive force 1,5V and resistance 0,25 Ohms and one resistor with resistance 2,5 Ohm are associated in such a way that the 2.5- resistor dissipates the greatest energy per second, that is? Answer: 90W.

My solution:

If we make m groups of n generators we would have:

$$m\epsilon=(\frac{mr}{n}+R)i$$

$$i=\frac{1,5mn}{0,25m+2,5n}=\frac{6mn}{m+10n}=\frac{240}{40/n+10n}=\frac{24}{4/n+n}$$

We know by the mean-inequality that

$$4/n+n>=2\sqrt{4} =4 $$

This is possible because it occurs when:

$$4/n=n \rightarrow n=2, m=20$$

$$i=6A \rightarrow P=90W$$

But why do all the groups have the same number of resistors? Why does the circuit have only series or parallel associations? Why isn't there any Delta/Star or any other more complex associations? Is there any way to solve this exercise in the right way?

P.S. I'm really not sure if the best way to post this is in the Physics or Math Forum. I'm posting in the Physics one. Sorry if I'm wrong by that/

40 identical generators with electromotive force 1,5V and resistance 0,25 Ohms and one resistor with resistance 2,5 Ohm are associated in such a way that the 2.5- resistor dissipates the greatest energy per second, that is? Answer: 90W.

My solution:

If we make m groups of n generators we would have:

$$m\epsilon=(\frac{mr}{n}+R)i$$

$$i=\frac{1,5mn}{0,25m+2,5n}=\frac{6mn}{m+10n}=\frac{240}{40/n+10n}=\frac{24}{4/n+n}$$

We know by the mean-inequality that

$$4/n+n>=2\sqrt{4} =4 $$

This is possible because it occurs when:

$$4/n=n \rightarrow n=2, m=20$$

$$i=6A \rightarrow P=90W$$

But why do all the groups have the same number of resistors? Why does the circuit have only series or parallel associations? Why isn't there any Delta/Star or any other more complex associations? Is there any way to solve this exercise in the right way?

P.S. I'm really not sure if the best way to post this is in the Physics or Math Forum. I'm posting in the Physics one. Sorry if I'm wrong by that/