# Battery and bulb #anyqs

Ok, I’m ready to play.

When you watch this, what do you wonder?

## 12 comments

1. How much time actually passes from when the hand leaves the frame until the end of the video?

• So cool! You let the clip run long enough for me to think, “Wait. That light can’t possibly last forever. How long can the light possibly last?”

Great work also with the stable camera and the bare canvas. If you filmed the light all the way from start-up to burn-out (the third act) I’m prepared to award you a diploma from Dan Meyer’s Curriculum College He Made Up Just Now.

Pretend I have no idea what I’m doing here. What’s the math involved? That’s a 9V battery. I assume I need to know the lightbulb’s wattage. What next?

• My recall of the formulas for electricity is a bit rusty, so please feel free to correct any mis-recollections…

It looks like some sort of automotive headlight, so I am going to guess that the light is a 12V light. If the battery was fresh, we can probably look up the mAH rating of a typical 9V battery.

If we were to measure the bulb’s brightness over time, we could have some fun working to model algebraically, or we could plot it on a graph and call it a day.

I assume that the current in the circuit is proportional to the bulb’s brightness.

By calculating or approximating the area under the bulb brightness curve, and comparing that number to the mAH capacity of the battery, we can figure out how we should scale the vertical axis of the graph to have it portray the current flowing in the circuit over time.

The power consumption probably declines even more precipitously than the current, since power = watts = (Current ^ 2)(Resistance) and the current output by the battery declines as its voltage drops. However, from this information and our graph, we should be able to infer the likely resistance of the bulb (if we know when the bulb finally stopped glowing).

All in all, a nice meaty problem that should keep the kids engrossed for a while!

• @Dan: Glad to know the length of the clip communicated what I had hoped (I wondered if it was too long). I agree about the 3rd act. In progress…

The math: you could do it with only two mathematical ideas. Voltage = current * resistance, and the battery’s “capacity” (current drawn for a period of time). Battery capacity is rated in Amp-hours, so if you want to know hours, you have to figure out Amps (current) — which in this problem is constantly changing.

Whit’s approach below is sensible, and involves using a light sensor — also known as a solar cell (another fruitful avenue to pursue). We could also measure the bulb’s resistance current at different voltages. The second act might involve showing a voltmeter in the video so we could graph the battery’s discharge (possibly with the lamp off-screen, so as not to give anything away). Then we could use the video voltage and our measured resistance data to approximate the current drawn. After that it’s an integration problem. (I teach an algebra-based program, but an approximate sum is not out of reach, and a decent way to introduce analog-to-digital conversion).

Along the way, we’ll need to wrestle with what exactly voltage and current are. I’m hoping that this will turn out to be a “generative question“.

• @Whit: I would approach it much as you did. I like your idea about measuring brightness — I might do this, with solar cells, as a way to inject more student practice with voltmeters. Measuring light is a tricky and approximate thing, since it is dependent on distance from the source, surface area of the thing it falls on, and material of the thing it falls on. If I play my cards carefully, it might even get us talking about why sometimes relative measurements are more useful than absolute ones (an idea my students tend to find despicable).

Brightness varies with power. So it is affected by current, for sure, but also by the bulb’s resistance. More current means more heat which means more resistance which means less current, so there is a bit of a negative feedback effect. Good stuff.

One of the wonderful things about this is the problem of when it “stops glowing.” That will be dependent on the sensitivity of each person’s eyes (see above about measuring light). Also, current continues to flow even after the bulb isn’t visibly emitting light… in fact, at low voltages, the bulb’s resistance approaches a short.

• @Joss: That’s interesting. What inspired that question? I’m curious what you’re going to use the answer for… the video is playing at 4x normal speed. In a previous take I overlaid the time on the video but decided to take it off because I think it belongs in “act 2″… I’m also inspired by Michael Doyle’s manifesto about uncalibrated thermometers.

• Hi Mylene, My first instinct was to wonder if the play speed after the hands were removed was the same as when we saw the hands. Once armed with that information I was going to take the mAh of a typical 9V battery and see if I could figure out the best way to determine the bulb resistance (which isn’t actually linear with temp anyway so there’s another wrinkle).

• @Joss: I gotcha. Yes, in earlier takes I did speed up after there was “nothing going on.” My raw footage shows noticeable dimming of the bulb. I decided to cut it before the dimming became noticeable, again in the interests of not precluding questions…

You’re right about the bulb resistance. This problem is wrinkly all over.

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3. Sorry, my first two reactions were
Where did you get the screw-block?
Who still has incandescent light bulbs?

After that came
What is the temperature of the filament?
Is that a rechargeable battery, or did you just produce a lot of trash?

The questions you probably wanted me to ask (having to do with time or power or something) were definitely way down the list.

• *grin* Thanks for the perspective. That style of terminal block is called a barrier block, search Newark or Digikey and you’ll find thousands of them in the \$3-5 range (for example). You’d be surprised about the incandescent bulbs. They’re everywhere in automotive, heavy-equipment, and industrial indicators. They’re slowly being replaced with LEDs but until recently there were many environments (especially dirty, dusty, or underwater) where LEDs could not be manufactured in high enough power densities).

Temperature of the filament is a darn good question, I hope to get the students talking about the relationships between heat, light, and power (color temperature would be a bonus, but probably too far outside their daily experience to register, unless someone’s into photography). And you’re right, it’s a primary cell… although it had a good life, being used for quite a number of takes. The battery is definitely not fresh in that video; I decided no one would be likely to check. Rechargeable batteries are, of course, eminently sensible, especially since I think I will re-shoot this with single-cells (AA maybe) and let students experiment with different sizes and combinations themselves.

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