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How to configure them
There are two different ways of configuring your own battery pack.
Connecting in series
Connecting batteries in series will cause the voltages of each of your batteries to be additive while the capacity will stay the same. To wire your batteries in series, you connect the positive terminal of one battery to the negative terminal of the next battery.
For example, if two NiMH AA batteries (~1.5V @ 2000mAH) are wired in series you will have a battery pack capable of supplying 3V @ 2000mAH. 1.5V + 1.5V = 3V
Connecting in parallel
Connecting batteries in parallel will cause the capacity of your batteries to be additive while the voltage will stay the same. To wire your batteries in parallel, you connect the positive terminal of one battery to the positive terminal of the next battery, and the negative terminal of the first battery to the negative terminal of the second. In other words, you will connect "like" terminals. Positive to positive and negative to negative.
NOTE: Never build a battery pack consisting of different kinds of batteries (different form factors, different chemistry), for example: NiMH with Alkaline, Lithium Polymer with Lead Acid, Lithium with Alkaline, coin cells with AAs, AAAs with Ds, and so on.
Mixing Series and Parallel
You can also create a battery pack that is mixes series and parallel configuration. If you know exactly how much voltage you'd like and how much capacity you'd like to provide, you can put your batteries in series and parallel to achieve that. The photo below shows two sets of two batteries, first put in parallel and then put in series with each to provide increased voltage AND capacity.
Here it is in detail (1.5V @ (2000mAH + 2000mAH)) in series with (1.5V @ (2000mAH + 2000mAH)) = 3.0V @ 4000mAH.
What to look for
There are three things to consider when looking at which batteries are the best fit for your project: voltage, capacity, capability, and power density.
Do the batteries supply enough voltage to make my electronics happy? All electronics components have a range of voltage in which they are comfortable operating, do these batteries supply a voltage within the range of all my components in the circuit? The most common operating voltages for microcontrollers and digital processors are 5V and 3.3V so this usually makes it easy. If you are not sure what the operating voltage of a particular component is, read its datasheet. Octopart is your friend.
The nominal voltage of a battery is often advertised on the battery itself.
The capacity of a battery is measured in amp-hours (Ah or mAh for milliamp-hours). For instance, if a 9V NiMH battery has a capacity of 150mAh in theory you can draw a constant 15mA from this battery and it should in theory run for 10 hours. 150mAh / 15mA = 10 hours
The capacity of a battery is often advertised on the battery itself or its packaging. It is denoted in mAh or AH. Alkaline batteries and many coin cells however do not advertise this.
The power capability of a battery is measured in coulombs and denoted by a C. You will NOT find this measurement advertised on the battery or its packaging but you can often find a rough estimate online and a more accurate measurements through the battery manufacturer's datasheet, if they are so kind.
Power density is the power a battery is able to supply in relation to its weight. The power is measured in watts (W) and is calculated by multiplying voltage by amperage or in this case, the nominal voltage by its capacity. The product is a value in Wh or watt-hours. The weight of a battery is measured in kilograms (kg). So, the power density of a battery can be something like 50Wh/kg. A high number means it can supply a lot of power for its size. Small and powerful is often ideal. Again, this is not advertised on a battery or its packaging but wikipedia will often give you a rough value.
Battery Chemistry Types
Lead Acid batteries usually come in the form of a big, hulking black box. They provide a lot of power, are rechargeable, but they however weight a lot. You can find them most often in automobiles, boats, scooters, motorcycles, etc. Lead acids are made up 2V cells, so you will find them with a voltage in multiples of 2V with the most common ones being 6V, 12V, 18V, and 24V.
Power Capability: +10C
These probably are the batteries most people are familiar with. They are very common, disposable batteries that can be purchased at just about anywhere. The cells are 1.5V and come in all sizes and shapes that include: coin cells, AAA, AA, C, D, 6V lantern batteries, and 9V.
Power Capability: 0.1C
NiCd batteries, or "ni-cads" are the first family of small rechargeable batteries. They come in 1.2V cells and can be found in packages that are multiples of this. They can be found in old wireless phones and remote control cars. They are also available in common sizes like coin cells, AAA, AA, C, D, and 9V. Unfortunately, their toxicity make them a poor alternative to safer and more superior rechargeables like the NiMH.
Pros: Rechargeable, cheap, and hold their charge a long time
NiMH (Nickel Metal Hydride)
NiMH batteries are a form of rechargeable batteries that are a great replacement for alkalines or "ni-cads". They come in common sizes such as AAA, AA, C, D, and 9V. They're cells are a nominal voltage of 1.2V but when fully charged they approach 1.4-1.5V.
Power Capability: 0.2C
Li-ion (Lithium-Ion) and Li-Poly (Lithium Polymer)
Lithium Ion and Lithium Polymer batteries are the newest rechargeables and have found their way into almost every piece of new consumer electronics. They are light weigh and really pack a punch in terms of power capability and density. Both types of battery chemistry require special circuitry for charging. You are unable to purchase Li-ion cells by themselves and will only find them by removing from things like cell phones and camcorders and using the electronics itself as the base charger. You can however purchase LiPo batteries from several distributors.
SparkFun also has a nice LiPo charger of their own on the market that I can safely say works quite well, SKU PRT-08293.
The cells are 3.6V and are commonly packaged in 3.6V and 7.2V.
Power Capability: 1-10C
Lithium Batteries and Coin Cells
Lithium batteries come in 3V cells. Coin cells are often very small and can be found in different battery chemistry, such as alkaline, zinc, and silver oxide with voltages per cell being either 1.5V or 3V. Coin cells are often used for hearing-aids, watches, electronic dog collars, and very low power electronics. Both come in varying sizes and capacities. Most types of these batteries aren't rechargeable so its very easy to choose them for their small size and burn through them in no time.
PowerStream is the only distributor I'm aware of that sells rechargeable Lithium coin cells in common coin cell sizes and also has a charger available. The nominal voltage of rechargeable coin cells is 3.7 volts.
Power Capability: 0.005C - 0.01C
A DC-DC converter is a circuit that converts a source of direct current (DC) from one voltage to another regulated DC voltage. The voltage of the source can either be boosted to a higher regulated voltage, this type is known as a step-up circuit, or the voltage of the source can be throttled to a lower regulated voltage, this type is known as a step-down circuit.
The reason for mentioning this is that very often you will want to run your digital electronics off batteries and yet it's very rare that a battery pack will supply your typical 5V or 3.3V. A DC-DC converter will supply the voltage you need steadily and efficiently.
Bodhi Labs is the creator of a variety of step-up battery packs that can be purchased through their website and are often in stock at the NYU computer store.
Sparkfun also sells a few step-up breakout boards.
Curious how long your Arduino will run off THOSE batteries while also using THAT electronic device? Well, Rob Faludi, being the resourceful man that he is, created tables that answer just those questions. Currently he has a slew of tests results from the Arduino and Xbee. He also has the Arduino and Processing code available if you wish to contribute to the table.
Battery Charging Station
Here at ITP we have three on-floor charging stations for rechargeable batteries.
Check out the notes on the Battery Charging Station page.