It is not just about high discharge. In return you also get fast recharge. Something that can suck in a large chunk of power, hold it for a short time, and then dump it out again rather quickly has certain advantages. Consider the energy storage system for regenerative braking, for example, which needs to absorb a lot of energy quickly -- the trick is then figuring out what to discharge it into, starting a vehicle rolling is the prime candidate but there may be other uses of an intermediate storage device like this.

In most cases I think that this will not displace Li-ion but would instead augment the existing battery setup.

Yeh, that's the really cool bit-- would you be okay with your iPhone only getting an hour of battery life if you could fully charge it in a couple of seconds?

I mean, obviously not, but it's interesting to think about.

But what about a hybrid system where you could add an hour or two of usage in that first few seconds of charging?

Would be great during a layover in a typical US airport where you might have to sit on the floor in a corner to use a power outlet. You could plug in for 10s to fill the cap, eat lunch while the cap charges the battery for an hour, plug in again for 10s before you fly out having something close to a full battery.

A cellphone battery is say 1 Amp Hour. Assume an equivalent capacitor is 3600 Amps for a second. Assume the capacitor is charged to 10x the Voltage, and is charged in 10 seconds. That needs 36 Amps - copper wires a bit thicker than those in a kettle cord. Bad approximations made, but right order I think.

Also there are real safety issues with something that can be charged that fast, because it usually implies it can be discharged faster. A shorted Li ion battery may burn, but a low-resistance capacitor will cause an explosion. Capacitors are fun :-)

An iPhone battery is roughly 1400mAh at 3.7V, which gives 5.2Wh or 18720 watt-seconds. A standard power outlet in the US supplies 15A at 120V, for a maximum of 1800 watts. So if you could charge your phone using the maximum power available from a standard outlet, it would take roughly 10 seconds. A typical laptop might take about 1-2 minutes. (That's assuming 100% efficiency, which is unrealistic.)

He's talking about the wire to the battery, not from the outlet.

Interesting. You could basically have the same fallback profile of a gas/electric hybrid vehicle.

Even if it only has 1/8 the energy density, it might have less than 1/8th the weight. If 8 graphene capacitors = 1 LiIon battery, it might be a lot lighter. That could could for a lot in some circumstances. (Mobile computing devices not being one of them)

Electric cars/tools/machinery.

camera flash.