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Here is a question that a friend asked me. He had to an experiment in school and do some calculations afterwards. Those calculations require maximal current that the DC source can produce. He has measured the maximal currents for two separate sources but forgot to measure it for both connected in series.

If maximal current of one battery is $a$ and maximal current of other battery is $b$, what will be the maximal current if one connects these batteries in series?

I could imagine the equation system: $$I=\frac{\varepsilon_1 + \varepsilon_2}{r_1+r_2}$$ $$I_1=\frac{\varepsilon_1}{r_1}$$ $$I_2=\frac{\varepsilon_1}{r_1}$$ where $I$ is for current, $\varepsilon$ for electromotive force and $r$ for inner resistance.

But it seems to have too many unknowns. And I'm not even sure if it's correct to describe the system in this way.

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closed as too localized by dmckee Jun 4 '13 at 18:31

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Does your friend only have values for the currents $I_1$ and $I_2$, not also the voltages of the two sources? – Will Jun 4 '13 at 17:27
This calls for application of Kirchhoff's circuit laws. – dmckee Jun 4 '13 at 17:30
@Will that is all the information he supplied. – Juris Jun 4 '13 at 17:48
@dmckee, as far as Kirchhoff's theory goes, I agree to Will's answer. But maybe you can demonstrate application you had in mind? – Juris Jun 4 '13 at 18:08
I had rather assumed that you had enough data. Without either the potentials at peak currents or a separate understanding of the internal resistances you are stuck. – dmckee Jun 4 '13 at 18:29

Without further information, it cannot be solved. That is, one cannot write

$I = F(I_1,I_2)$

a function of $I_1$ and $I_2$ alone. The best one could do it rewrite what you have above as

$I = \frac{r_1}{r_1+r_2}I_1 + \frac{r_2}{r_1+r_2}I_2$

which still requires knowledge of the internal resistance of the batteries.

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Yes, that's about as much as I can get out from those equations myself. – Juris Jun 4 '13 at 18:06

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