Power density is a measure of power output per unit volume. While it is not as commonly used a measurement as energy density, it is still useful for conversations about energy systems (often for portable applications like transportation). It's helpful to understand power density vs. energy density.
If a system has a high power density, than it can output large amounts of energy based on its volume. For example, a tiny capacitor may have the same power output as a large battery. Because the capacitor is so much smaller, it has a higher power density. Since they release their energy quickly, high power density systems can also recharge quickly.
An example application of this type of energy storage is a camera flash. It has to be small enough to fit inside the camera (or cell phone) but have a high enough power output to light up the subject of your photo. This makes a system with a high power density ideal.
Power density is also why it takes time to recharge your flash in between photos. The battery has a lower power density than the capacitor in the flash. This means that the recharge time for the flash is limited by the power output of the battery, rather than the power output of the flash. The energy density of the battery however is higher than the energy density of the capacitor.
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