Differences of lithium ion battery, LifePo4 and Lithium polymer batteries
Three Major types of lithium battery available for most projects: lithium ion (li-ion), lithium iron phosphate (LiFePO4), and lithium polymer battery (li-po).
Lithium ion li-ion battery
Li-ion is the most common one. There are a few slightly different varieties, but they all share similar properties: high energy density, fairly safe when not abused, and reasonably inexpensive. Almost all electric vehicle makers use li-ion batteries. Li-ion is likely the best type to use on most of your projects, unless the advantages of the other two types are required.
lithium iron phosphate LiFePO4 batteries
LiFePO4 batteries are less energy dense, making them bigger and heavier than li-ion. Most LiFePO4 varieties also have lower discharge ratings, making them less powerful. LiFePO4 are also more expensive than li-ion, but they are the safest lithium variety and have extremely long cycle life.
Li-po batteries are the kind used in R/C drones. They have the highest power level, but they can also be extremely dangerous if not charged and discharged carefully. These are needed for extremely high power projects but extra care must be taken to ensure safe conditions.
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