# Sampling an AC Source with a DC meter

## Abstract

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.

## Results

* 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.