 Solution

An ordinary capacitor stores energy by separating charge across a dielectric: $E=C{V}^2/2$ and $Q=CV$. Electronic charge redistribution is rapid, giving high specific power, but the dielectric breakdown field and modest capacitance limit specific energy. Series resistance limits pulse power and produces heating; a large nominal capacitance does not remove those losses.

A supercapacitor has a much larger interfacial area and nanometre-scale charge separation. An electric double-layer capacitor stores charge without a bulk redox transformation; pseudocapacitance adds sufficiently fast surface or near-surface redox storage. ion motion in pores, electrolyte stability and series resistance constrain its response. Its specific energy usually exceeds an ordinary capacitor's while high specific power and cycling durability remain possible.

An electric battery stores chemical free energy through coupled electrode oxidation-reduction reactions. It can store substantial energy per mass, but charge transfer, ionic transport, diffusion and heat removal constrain rapid discharge. The terminal voltage and accessible capacity depend on discharge rate and state of charge. Accordingly the plotted order follows the storage and transport mechanisms; it is not a claim that every battery has less power than every supercapacitor.