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My wife has a tabletop light she uses for quilting work. She wants to take it with her to a class that has no access to AC. Output from AC plug to lamp is 12V, 3A.

I have searched for power formulas and I think this means it uses 36 Watts per hour or 3000 mAh. I would like to know what size portable power supply I would need to keep her lamp working for an 8 hour class.

Am I correct in just taking 8 hours times 3000 mAh = 24,000 mAh capacity would work? Or 8 hours times 36 Wh = 288 Wh capacity would work?

Thank you for your input to this question!!

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    \$\begingroup\$ You are correct, you need 36 Wh or 24,000 mAh at 12 volts. The lamp uses 36 watts or 36 joules per second, not 36 watts per hour or 36 joules per second per hour. \$\endgroup\$ Oct 21 '18 at 17:04
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    \$\begingroup\$ Your math is OK. Your terminology is a bit off (as TimWescott says). But sometimes the ratings on devices like this are the maximum rather than the average. Average is what you would want to use for sizing the battery pack. So it would be nice to measure the actual power usage somehow. You might not really need to supply 288 Wh. Also, if you use an LED lamp, you will likely only need 1W or at most a few W. So the battery could be much smaller. I wonder if your wife's light uses an incandescent bulb? Can the bulb be changed? Anyway, good luck. \$\endgroup\$
    – mkeith
    Oct 21 '18 at 17:23
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I think this means it uses 36 Watts per hour or 3000 mAh.

It means it uses 36 Watts, period. In an hour it'll use 3000mAh, yes -- but a mAh is a measure of charge (one mAh is 3.6 Coloumbs, if you want to be irritatingly correct), not power.

The light will probably work fine if you just connect it to a sealed lead-acid cell. The voltage it gets will only be nominally 12V (it'll range from 13.5 down to 12 as the battery discharges), but that will probably be OK.

Battery capacity is rated ambitiously -- if you fully drain a battery you significantly decrease it's lifetime. Get a sealed lead-acid that's advertised as having a capacity about 150% more than your calculation. Then make sure you're charging it with a good charger (I'd use a model airplane charger that has a lead-acid mode -- the Great Planes Triton should be good enough).

My suggested capacity gets you around 22 pounds of battery -- that may be more than she wants to lug around.

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    \$\begingroup\$ "... but a mAh is a measure of energy ..." - No, it's a measure of charge. Wh is a measure of energy. You can easily see this as follows: a 12V 3Ah battery carries a lot more energy than a 1.5V 3Ah battery, so the 3Ah cannot be a measure of energy. \$\endgroup\$
    – marcelm
    Oct 21 '18 at 18:08
  • \$\begingroup\$ @marcelm Good catch, of course. I think Tim knows this fact well and just misspoke. But he should correct his language. This is a technical field and details matter. (I think Tim lives, or used to live, near me. I'm out in Damascus Oregon.) \$\endgroup\$
    – jonk
    Oct 21 '18 at 19:26
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Am I correct in just taking 8 hours times 3000 mAh = 24,000 mAh capacity would work? Or 8 hours times 36 Wh = 288 Wh capacity would work?

This is correct, these two statements are equivalent: 24 A-hr at 12 V is equal to 288 W-hr, just as 36 W consumed over 8 hours is equal to the same 288 W-hr.

Therefore, the solution to your power problem is a 12-V 24 A-h battery, which is about the size of the usual car battery. And therefore consider the corresponding weight of the power bank device. Designing a rechargeable and neat device out of raw battery has some engineering challenges, so in your case it is advisable to look for a consumer-grade solution.

There is an industry that serves this sector, it is "outdoor and recreation", they have portable power banks in the range of capacity you need, ~300 Whr and much more. Unfortunately these kind of devices also include DC-AC invertors to 120 or 220 V AC, which you don't need, and this adds to cost. Typical capacity of 12-V-only devices is marginally lower than you need for your wife's lamp. The best I could find is a 185 Wh power bank,

power bank 185 Whr

Maybe you will have a better luck in searching deeper. Unfortunately, manufacturers usually are not completely honest in their marketing efforts, and if some device with 5-12-20V output is "rated" as "50000 mAh", it likely means the mAh capacity either at 5V output, or at 3.7V Li-ion level.

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The energy required is 36Wh * 8 = 288Wh at minimum. The best energy density available at this moment is for Li-Po batteries of 150W/kg,see here the source, so your battery will be at least 2kg without the case and other circuits, for a lead acid battery (20Wh/kg) 15kg, for a NiCd battery (50Wh/kg) 6kg, and for a NiMh (75Wh/kg) 4kg.

It looks to me that you use a classic or halogen bulb, I doubt that you use a 35W led lamp for a table top so I would search for a compatible LED bulb that would drop the energy required around 8 times, down to 36Wh.

I also bet that the lamp can use DC voltage so you won't need a DC to AC converter.

For a 36Wh you will need a 3000maH battery , as a suggestion you can buy a cordless drill rated 10.8V (that charged goes above 12V) with a higher capacity with the advantage of having it's own charger and using it in weekends for home improvements.

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