Lab Experiment: Estimate the error in these measurements of Ohm's law

[ORF]

Homework Statement

calculate resistance, measuring current and voltage

Relevant Equations

Ohm Law, V = R*I

Hi,

I have measured a set of V-I values, and I have to provide the value of the resistance. I have used ac and dc current.

The circuit was quite simple:
power supply -> ammeter -> resistance -> [power supply]
wave generator -> ammeter -> resistance -> [wave generator]

Voltage was measured using an oscilloscope.

So, I think there are two ways of estimating the resistance, but they are not the same and I do not know which one should be used.

On one side, you may use Least Squares fit to estimate the best value for R. Is it correct to mix measurements with ac and dc current? How shall these measurements be combined?

On the other side, I though about using the definition of mean and variance for the set of "V_i / I _i" values .

Although the resistance mean value of is quite similar using one or the other, the error is not.

So, the questions are:
1. Should "V_i / I _i" be considered independent measurements, and therefore resistance should be calculated using the regular average and variance formulas? or should it be considered as a pair of correlated random variables, and R must be obtained from the fit of V-I plot?
2. Is it correct to combine ac and dc measurements?

Thank you in advance.

Regards,
ORF

 

[BvU]

Hi,

You have done two different experiments. So you want to keep them separate until you have an idea about matching and mismatching conditions.

If you vary one thing and measure something that depends on it, always make a plot.
Consider what are random errors and what are systematic errors.

1. Not really: I suppose you used the same meters (ammeter and oscilloscope), so their caliration error is common to all observations !
2. At the very end only. Suppose one says 220 $\pm$ 2 $\Omega$ and the other says 140 $\pm$ 20 $\Omega$ ?

 

[haruspex]

Should "V_i / I _i" be considered independent measurements, and therefore resistance should be calculated using the regular average and variance formulas? or should it be considered as a pair of correlated random variables, and R must be obtained from the fit of V-I plot?

If you plot y against x and get the slope from standard regression analysis, the algebra minimises Σ(Δy)². In effect, it assumes your x values are exact and the only errors are in y. A more even-handed approach minimises sum square of the distances from the plotted points to the regression line - i.e. as measured along the normal to the line.
More generally, if you can make a priori estimates in accuracies of the two sets of measurements, you can weight the x and y coordinates of the distances accordingly.

If you compute the V/I ratios and take the average, that is something else again. I don't recommend it, but I'd need to do some more analysis to justify that.