# Replace 12V 5A power supply with battery

I am buying a rgb led strip with the following technical details:

Voltage: 12 volts
Wattage: 60 watts


I want to connect this strip to a battery and don't know what will be the right one. I need the battery to last for 2 hours.

I been doing research and this are my assumptions based on what I have researched. Please let me know if I am wrong.

1. I know that volts * amp-hour = watt-hour If I plot the technical details into the formula then I know that I will be needing 5 amps per hour.

2. I now need a battery of 12 volts that can output 5 amps per hour. When looking into the internet I see a lot the term Ah which means amps per hour. Based on this needs I found this battery: Elk ELK-1280 12V 8Ah Sealed Lead Acid Battery.

I read that if a battery has a capacity of 2Ah then if you discharge it at 2 amps per hour it will drain in one hour. If you discharge that same battery at 1 amps per hour (half of that) then it will last twice. If you discharge it at 4 amps per hour then it will last 30 minutes.

1. I assume that 8Ah means that if the battery where to use 8 amps in an hour it will drain in that hour. But because I will be using 5 instead of 8 then I know that I will be able to have the battery last longer about 1.4 hours.

All the batteries with this capacity that I am looking for are often big and heavy. Then I came across Hiyadeal Portable 12V 9800mAh Li-ion Rechargeable Battery Pack. That battery is only 1 pound! That battery claims to deliver 9800mAh or 9.8 Amps per hour. That means that if I where to use this battery because I only need 5 amps then it will last for about 2 hours?

Let's clear up some terminology first. An Amp is not a discrete quantity of energy. It is actually a quantity of electrons per time. Therefore, you don't say "Amps per hour". I like to use the analogy that Amps of current is like speed in your car. If you drove your car for an hour at 60mph (pardon my English unit assumption) and someone asked you about your drive, you wouldn't say "I drove 60mph per hour". That would be silly. Instead you would say "I drove 60mph for an hour."

It's the same with current. A battery doesn't supply 5 Amps per hour, it provides 5 Amps for an hour. Furthermore, a battery that has supplied 5 Amps for an hour has provided 5 Amp-hours (5Ah) of charge. An Amp-hour is an actual discrete quantity. It represents the capacity of the battery.

So you need a battery that can provide 5 Amps for 2 hours at 12V. That's 10 Amp-hours total. More specifically, since it's 12V: $$5A*2hours*12V = 120Wh$$
Of course, you would never want to buy a battery that can only provide exactly the capacity you need. You want some capacity in reserve. So let's double it and say you probably want a 240Wh battery. That way, you'll only use 50% of the capacity in one session.

The Li-ion battery you mentioned in your question has a 9800mAh capacity at 12V. That works out to 117.6Wh. Almost enough to last for two hours with a 5A current draw. As long as you understand what you're doing with a Li-ion battery, that should work, but I would recommend putting two in parallel to double the capacity. When you put two batteries in parallel, their voltage stays the same (12V) but the total capacity doubles (9800mAh * 2 = 19.6Ah).

EDIT: Looking at the website for that Li-ion battery, it is not clear what its continuous current capability is. It may not be able to supply 5A of current continuously without overheating. Without a datasheet or more technical specs, it's probably not safe to use.

One other note, batteries are not perfect energy sources. As you discharge them, their voltage lowers, their internal resistance increases, and their ability to supply current decreases. The more current you draw at a time, the more these negative effects occur. What all that means is a 10Ah battery may not actually supply a full 10Ah before the battery is flat. This is another reason to get a battery that has a larger capacity than the math dictates.

• An amp-hour is not a unit of energy. Multiplying the amp-hours by the voltage yields the energy in units of watt-hours. Also, note that the Li-ion rechargeable battery called out in the question is specified(see the description in the link) as having a maximum current capability of 1 amp so it is not suitable for this application.,\ – Barry Oct 22 '14 at 20:11
• Also note that the Li-ion battery specified in the question has a maximum capability of only 1 amp (see the Product Description in the link). Therefore it is not suitable for this application. – Barry Oct 22 '14 at 20:17
• @Barry, yep, I noticed my error right after posting my answer and corrected it in the 3rd sentence (see the edit history). But I failed to fix it in the 2nd paragraph at that time. Thank you for pointing that out. As for the Li-ion battery, I added an edit earlier that warns against using that battery without more information about it. Honestly, I wouldn't trust the product description in an Amazon link either way. – Dan Laks Oct 22 '14 at 20:24

To deliver $60$W with a $12$V battery the battery will need to continuously discharge

$$I = \frac{P}{V} = \frac{60\text{W}}{12\text{V}} = 5\text{A}$$

Note that this is amps, not amps per hour.

The unit Ah is an amp-hour (a unit of electric charge), which is not the same as amps per hour. To calculate how long a battery with a given Ah rating can discharge a given current $I$ in amps simply multiply the current $I$ by the time duration $t$ in hours. In your case you need a battery with a rating of

$$It = 5\text{A}\times 2\text{ hours} = 10\text{Ah}$$

None of the batteries you have identified have a sufficient Ah rating. The $9.8$Ah battery you mention will be able to discharge $5$A for only

$$t = \frac{9.8\text{Ah}}{5\text{A}} = 1.96\text{ hours}$$

This is close to 2 hours but not quite.

Additionally, all of this assumes that the battery's maximum discharge current is $\geq 5$A. If not then the battery will not be able to safely discharge the $5$A you desire.

In short, look for a $12$V battery with $> 10$Ah capacity and $> 5$A maximum discharge current in order to deliver $60$W for at least $2$ hours.