# Internal Resistance

If I do 5 trials of measuring voltage and current of a circuit (with different resistors for each trial), how would I find the inner resistance of the power source?

Dick
Homework Helper
Internal resistance can be calculated from the current that would flow if there were no external resistance. How could you extrapolate that value from your data?

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How could you extrapolate that value from your data?

Good question. I'm trying to figure that out.

Dick
Homework Helper
Well, how about this. If you make a graph of external resistance vs current, how could you extrapolate to zero external resistance?

Well, how about this. If you make a graph of external resistance vs current, how could you extrapolate to zero external resistance?

A Best fit line?

Dick
Homework Helper
Yessssss. And what intercept will be of interest?

x-intercept?

Dick
Homework Helper
If the line corresponding to zero external resistance is the x-axis, yes. I would maybe graph it the other way around, but it's your choice.

We have the equation : Ri+Re=E/I
where Ri is internal resistance, Ro - external resistance, E emf and I : current.
E can be measured as open circuit voltage or when the current is zero. In fact if you measure the voltage, there's some current going through, but it is very small and can be negligible. So theoretically, with only one value of Re, you can calculate Ri.
If the circuit involves a battery, it may be more complicated for the concentration overvoltage.

Never mind. I think I got it. Thanks for all of your help.

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Dick
Homework Helper
Hmm. I apologize - I've been having you graph and extrapolate a function which is not linear. Not the best way to reduce the data. I somehow had it upside down in my head. I think it's better to take Haiha's suggestion, (R_ext+R_int)=E/I. Your graph will also give you an approximate answer if you take the unloaded voltage of the battery and divide by your current. But it's probably better to take each data point independently. Sorry again!

I seem to be confused at what you want me to graph, now.

Dick
Homework Helper
I don't know that I want you to graph anything. Do you have a measurement of the voltage without any resistors? If you want to graph something try measured currents vs measured voltages. That should be linear.

I don't know that I want you to graph anything. Do you have a measurement of the voltage without any resistors? If you want to graph something try measured currents vs measured voltages. That should be linear.

The Voltage without external resistors is 5 V

I also have the equation of the Best-fit line for Voltage vs. Current

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Dick
Homework Helper
Good. Then let's take Haiha's suggestion. R_ext+R_int=E/I where the E is 5V. You know I for each value of R_ext. This will give you 5 estimates for R_int.

r = .542 Ω
r = .714 Ω
r = .891 Ω
r = 1.455 Ω
r = .889 Ω

Quite a big difference.

Dick