1
\$\begingroup\$

I am trying to power a 3 Watt light-bulb. I would like to calculate how long that light would run on a triple A battery versus a AA battery.

How do I do that?

\$\endgroup\$
  • \$\begingroup\$ Light bulb or LED? \$\endgroup\$ – Russell McMahon Jan 17 '15 at 10:50
2
\$\begingroup\$

A single battery? Not very long. You can look up battery datasheets. 3W at 1.5V is 2A.

Even with an AA battery, a 2A discharge current is off the chart. Maybe constant power you could get a few minutes. AAA would be worse.

enter image description here

Two fresh top-quality alkaline cells might be able to buy you 1/2 hour operating if you allowed the voltage to drop to 1V (that's constant current discharge, so much of the time you'd actually be getting between 3W and 2W. Constant power or AAA would be worse.

|improve this answer|||||
\$\endgroup\$
1
\$\begingroup\$

A decent quality AA battery will have about 2400mAh capacity. A similar quality AAA battery will have about 1200mAh capacity. So, for a given load, the AA will last about twice as long.

Your 3W light running off a single 1.5V battery will consume 3 / 1.5 = 2A of current, so will (nominally) last about 2.4/2 = 1.2 hours for the AA and 0.6 hours for the AAA. However, given that 2A is a very high current for these batteries, I wouldn't be surprised if you got 3/4 of that time or less. Another problem is that the voltage will drop quite quickly under that kind of load, so the light will dim quickly as well.

As to how you do it, there are some clues above. You should also look for a datasheet for your particular battery and examine the graphs provided. Decent battery manufacturers will give you useful graphs about how their batteries respond to different loads.

|improve this answer|||||
\$\endgroup\$
  • \$\begingroup\$ 3w bulb is likely an LED or CFL. They are not pure resistive loads like an incandescent bulb. There will be a power factor of less than 1 for these bulbs. Will that affect the "run time" of the battery? \$\endgroup\$ – Filek Jan 16 '15 at 22:12
  • \$\begingroup\$ @Filek Off the top of my head, I'm not sure. I'd want more information for a considered answer. My instinct though is to say "no" because I agree that it's probably a LED, and I don't think I've ever seen a LED described as a reactive load. Non-linear, yes, but not reactive. \$\endgroup\$ – markt Jan 16 '15 at 23:15
  • \$\begingroup\$ "Power factor" has no meaning for a DC source like a battery. \$\endgroup\$ – Brian Drummond Jan 17 '15 at 10:08
  • \$\begingroup\$ @BrianDrummond Agreed, but I've never looked at a CFL drive circuit (and I have no idea what it entails), so I wonder about circuit and battery interaction as the battery flattens hence hedging my bets. \$\endgroup\$ – markt Jan 17 '15 at 10:19
  • \$\begingroup\$ @BrianDrummond - If power factor has no effect on battery power, why do UPS backup battery systems give ratings in both watts and volt*amps? (I'm not challenging you, I'm just confused) \$\endgroup\$ – Filek Jan 18 '15 at 7:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.