# Electricity math! Need help planning for solar...

April 23, 2013 12:41 PM Subscribe

So instead of providing an answer, please help me by showing me how you got your result.
I have a 12v device that consumes 1W in idle mode, and 5W in active mode. How many "amp hours" am I looking at over a 24 hour period (always on). I am looking specifically for amp hours... I don't understand the relation between amps and amp hours yet.

Response by poster: Approximately 1 hour out of the entire 24.

posted by squirbel at 12:46 PM on April 23, 2013

posted by squirbel at 12:46 PM on April 23, 2013

Wolfram Alpha to the rescue!

((5watts/12volts) *1 hour + (1watt/12volts) *1 hour ) = 0.5 Ampere hours

posted by rockindata at 12:52 PM on April 23, 2013

((5watts/12volts) *1 hour + (1watt/12volts) *1 hour ) = 0.5 Ampere hours

posted by rockindata at 12:52 PM on April 23, 2013

Response by poster: Thank you so much! With that I'll be able to finish the rest of my calculations! :D Doh! Wolfram? XD

posted by squirbel at 12:53 PM on April 23, 2013

posted by squirbel at 12:53 PM on April 23, 2013

Best answer: Except it's 23 hours of idle time, not one. So:

5/12*1 + 1/12*23.

I would round it to 1/2 + 2 = 2.5 amp hours.

posted by LowellLarson at 12:54 PM on April 23, 2013

5/12*1 + 1/12*23.

I would round it to 1/2 + 2 = 2.5 amp hours.

posted by LowellLarson at 12:54 PM on April 23, 2013

Best answer: Except, you know, stupid things like getting the numbers right.

Try this!

((5watts/12volts) *1 hour + (1watts/12volts) *23 hours ) = 2.333 Ampere hours

posted by rockindata at 12:54 PM on April 23, 2013

Try this!

((5watts/12volts) *1 hour + (1watts/12volts) *23 hours ) = 2.333 Ampere hours

posted by rockindata at 12:54 PM on April 23, 2013

Best answer: Power = Voltage * Current (P=IE), so Current = Power / Voltage (I=P/E)

At idle, current = 1W / 12V = 1/12A = 83mA.

Active, current = 5W / 12V = 5/12A = 417mA.

If you're active for 1 hour, that's 1hr * 417mA = 417mAH (about 1/2AH)

If you're idle for 23 hours, that's 23hr * 83mA = 1916mAH (about 2AH)

You should be able to run your device on a 3AH battery (or larger), as long as you can average enough recharging every day. A bigger battery than necessary can hold extra charge, so even if you don't get 2.5AH one day, your system won't die.

If you put in a minimum-sized battery, then you can't take advantage of sunny days, and you might run out after a couple of cloudy ones.

posted by spacewrench at 12:56 PM on April 23, 2013

At idle, current = 1W / 12V = 1/12A = 83mA.

Active, current = 5W / 12V = 5/12A = 417mA.

If you're active for 1 hour, that's 1hr * 417mA = 417mAH (about 1/2AH)

If you're idle for 23 hours, that's 23hr * 83mA = 1916mAH (about 2AH)

You should be able to run your device on a 3AH battery (or larger), as long as you can average enough recharging every day. A bigger battery than necessary can hold extra charge, so even if you don't get 2.5AH one day, your system won't die.

If you put in a minimum-sized battery, then you can't take advantage of sunny days, and you might run out after a couple of cloudy ones.

posted by spacewrench at 12:56 PM on April 23, 2013

Best answer: So amp hours are amps consumed over an hour, 1 amp for 1 hour is 1 amp hour, 2 amps consumed for 5 hours is 10AH.

For DC, watts is volts times amps, which means amps is watts divided by volts (yay algebra!). So 1 hour in idle mode is 1 watt / 12 volts, and 1 hour in active mode is 5 watts / 12 volts.

So 1 hour of active mod and 23 hours of idle mode means...

(1 hour * 5 watts / 12 volts) + (23 hours * 1 watt / 12 volts)

or 5/12+23/12 = 28/12 or 2.3333... amp hours at 12 volts to drive this thing for a day.

posted by straw at 12:56 PM on April 23, 2013

For DC, watts is volts times amps, which means amps is watts divided by volts (yay algebra!). So 1 hour in idle mode is 1 watt / 12 volts, and 1 hour in active mode is 5 watts / 12 volts.

So 1 hour of active mod and 23 hours of idle mode means...

(1 hour * 5 watts / 12 volts) + (23 hours * 1 watt / 12 volts)

or 5/12+23/12 = 28/12 or 2.3333... amp hours at 12 volts to drive this thing for a day.

posted by straw at 12:56 PM on April 23, 2013

Response by poster: My device is a 12VDC and it has a power brick that allows it to plug into AC...

posted by squirbel at 1:00 PM on April 23, 2013

posted by squirbel at 1:00 PM on April 23, 2013

The water analogy:

Amps are chunks of electrical charge per second. Like 100 golf balls per second. Or 100 liters per second.

Amp hours: So many amps times so much time.

100 liters per second * 1 hour = ( 100 liters / second ) * 3600 seconds = 360,000 liters.

(Only, amps are Coulombs per second, where a coulomb is 6.2 ×10e18 electrons.)

So if it was

100 Amps * 1 hour = (100 Coulombs / second ) 3600 seconds = 360,000 Coulombs.

posted by sebastienbailard at 1:33 PM on April 23, 2013

Amps are chunks of electrical charge per second. Like 100 golf balls per second. Or 100 liters per second.

Amp hours: So many amps times so much time.

100 liters per second * 1 hour = ( 100 liters / second ) * 3600 seconds = 360,000 liters.

(Only, amps are Coulombs per second, where a coulomb is 6.2 ×10e18 electrons.)

So if it was

100 Amps * 1 hour = (100 Coulombs / second ) 3600 seconds = 360,000 Coulombs.

posted by sebastienbailard at 1:33 PM on April 23, 2013

Response by poster: Imagine swirly, confused eyes. Thanks for the explanation!

posted by squirbel at 1:39 PM on April 23, 2013

posted by squirbel at 1:39 PM on April 23, 2013

Just to be pedantic, if it's a 12V device that can be powered by a car battery or through an accessory outlet (AKA cigarette lighter), it operates at a nominal 13.8V. Just substitute for the 12 in the formulas above.

posted by tommasz at 1:54 PM on April 23, 2013

posted by tommasz at 1:54 PM on April 23, 2013

It's confusing, I know. If you use the water analogy, Amps might map to something like 'garden hoses', as in 10 hoses is a 10X bigger flow than 1 hose. And then hose-hours means 'enough pressurized water to run one hose for one hour'. You fill your water tower up with many hose-hours worth of pressurized water. With electricity amp-hours means 'enough stored electrical energy to push 1 Amp worth of electricity for one hour'. You fill your battery up with many amp-hours worth of electrical energy.

(at a given 'pressure', or voltage, which is 12V in this case. The higher the pressure, the faster you go through water, so the more water you need to make up one hose-hour at that pressure. Thus one amp-hour in a 12V battery is a smaller quantity of energy than one amp-hour in a 24V battery -- half, in fact.)

When doing your planning be sure to overdesign for your requirements. A 3Ah battery may only give you 2Ah in practice, and there may be extra drains and losses that increase the amount of energy you need.

posted by PercussivePaul at 2:27 PM on April 23, 2013

(at a given 'pressure', or voltage, which is 12V in this case. The higher the pressure, the faster you go through water, so the more water you need to make up one hose-hour at that pressure. Thus one amp-hour in a 12V battery is a smaller quantity of energy than one amp-hour in a 24V battery -- half, in fact.)

When doing your planning be sure to overdesign for your requirements. A 3Ah battery may only give you 2Ah in practice, and there may be extra drains and losses that increase the amount of energy you need.

posted by PercussivePaul at 2:27 PM on April 23, 2013

Since you're planning for solar, PercussivePaul's last paragraph is a good one to keep in mind. A battery's amp-hour rating is usually a best-case number— it's based on whatever situation gives the best number, typically a fairly slow discharge. (A good battery spec sheet will list different AH numbers for different rates of discharge.)

Also, you probably don't want to plan to fully discharge your battery very often — lead-acid batteries, in particular,

posted by hattifattener at 11:24 PM on April 23, 2013

Also, you probably don't want to plan to fully discharge your battery very often — lead-acid batteries, in particular,

*hate*deep discharge cycles (deep-cycle marine batteries or AGM cells or etc. do better than car batteries, but deep-cycling is still not something you want to do regularly unless you plan to replace the battery a lot). Some other chemistries, like lithium-ion, don't mind being deep-cycled as much, but might have other drawbacks, like cost. So you might need to size your battery so that you don't expect to draw it down below, say, 40% very often. Yes, this is all super complicated. :/posted by hattifattener at 11:24 PM on April 23, 2013

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posted by rockindata at 12:43 PM on April 23, 2013