# Gas station without pumps

## 2013 February 12

### Battery internal resistance lab and Chapter 21 homework

Filed under: home school — gasstationwithoutpumps @ 17:49
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In our home-school physics class today, my son and I did two things: comparing answers on homework questions and a lab measuring the internal resistance of a battery.  I only had time to read Chapter 20 of  Matter and Interactions this morning, and only finished about half the problems.  I’ll have to finish them and compare answers with my son later. He’s already finished—he found these problems as easy as the ones in Chapter 19, but much more fun.  I suspect that Chapter 19 is one of those things that only a physicist can love—those of us who have more of an engineering mindset just find it tedious make-work.

The internal resistance of the battery was a simple experiment: we put known resistors across the battery pack and measured the resulting voltage.

The top circuit shows the setup we used—the bottom shows the equivalent circuit we were modeling.

I also measured the short-circuit current (briefly) with an ammeter.

The data was much noisier than I had expected, probably because the “switch” just pushed one battery away from contact, and the contact resistance between the battery holder and the batteries varied. We tried cleaning the contacts on the battery holder and on the batteries, but the noisy data were after that cleaning.  The noise is probably not due to self-heating of the resistors, as it was highest for the larger resistors.

The load line using the open-circuit voltage and short-circuit current look reasonable, but many of the measured voltages corresponded to a lower current, and fitting just the data points that exclude the short-circuit current does not produce a reasonable load line, though the estimated internal resistance is not too far off.

The battery-measurement lab took longer than I expected, because the data wasn’t as clean as I expected.  It might be worth trying again with a different battery holder, and a better switch, to see if the problems were just with the crummy contacts on the battery holder.  Variations of 0.5Ω in the resistance of the contacts would throw the measurements off by this much.

Chapter 21 of Matter and Interactions appears to be about magnetic force (though we don’t get to inductors until Chapter 23).  I find magnetism much more confusing than electricity, so I suspect we won’t be as quick with Chapters 21–23 as we were with Chapter 20. Problems for Chapter 21:  21P38, 21P39, 21P40, 21P44, 21P50, 21P60, 21P61, 21P66, 21P69, 21P71, 21P72, 21P79, 21P80, 21P90, 21P103, 21P105 (computational).