Sampling an AC Source with a DC meter


An undergraduate level experiment is described to demonstrate the role of probabilistic observations in physics. A capacitor and a DC voltmeter are used to randomly sample an AC voltage source. The resulting probability distribution is analyzed to extract information about the AC source. Different characteristic probability distributions arising from various AC waveforms are calculated and experimentally measured. The reconstruction of the AC waveform is demonstrated from the measured probability distribution under certain restricted circumstances. The results are also compared with a simulated data sample. We propose this as a pedagogical tool to teach probabilistic measurements and their manipulations.

* physics/0301002 Click here for the postscript file (archive physics/0301002) submitted to American J Physics

* prob.c Click here for the C programme in Appendix of paper

* bin.c ; binning of data using bisection

* chinl.c ; chi-squared fit to data binned using bin.c, using Numerical Recipes routines
Note: Numerical Recipes C are needed to compile and run the chisq-fit programme. Please note that NRC are copyright-protected software; it must be legally loaded on your system before you can run the above program.

Experimental data (from Amritsar group)

Click here for 499-points 8.3 V data

Simulated data (using Numerical Recipes' ran2.c)

Click here for 499-points 8.3 V data
Click here for 9980-points 8.3 V data
Click here for 499-points 16.4 V data
Click here for 9980-points 16.4 V data

Note: These are as-is-where-is generated data. I've included the unsorted set because in principle you can analyse parts of this sample just as well. You may want to sort it using the sort command of your editor to see the trend of frequencies of different voltage values.


* bin8.eps Click here for graphical results of the binning with 8V data

* chi8.eps Click here for the chi squared fit to the 8 V data

In both graphs, I refers to experimental 500* samples data; II to simulated 500 samples data and III to 10,000 samples simulated data.

(*) Since the Amritsar data set had 499 and not 500 data samples, the simulated data were generated accordingly.