The Mophie 4000mAh battery is about the size of the original iPod, and I carry it in my accessory bag enclosed in my iPod's original Timbuk2 carrycase. The Mophie's aluminum exterior is nicely finished and has two ports - one for charging the Mophie itself and the other a standard desktop/laptop USB port from which to charge cellphones and similar items. The one other external feature is a rectangular power status button that is flush with the side of the case.
Pressing the power status button lights up one to 4 LED's that indicate the level of charge available in the Mophie battery. If no LED's light up the Mophie is completely discharged. I checked Mophie's site and the user manual but could not find an estimate of the time required to charge the Mophie itself from zero to 100 percent. Since my Mophie battery did not include an AC adapter, the charging time required would depend on the current available from the charging source. Some low-power USB ports may not charge the Mophie at all and some may charge it very slowly, but fastest results will be obtained with a USB wall charger that outputs 2 amps of current or better.
I did a usage test to determine how long a fully-charged 4000mAh Mophie would last when powering the pocket-size 'iStreamer' digital-to-analog converter, when the iStreamer is connected to an iPhone and charging the iPhone at the same time. The iStreamer gets a digital signal from the iPhone and outputs an analog signal to feed to a headphone amp or to a powered desktop speaker system. The iStreamer is a very low-power device and should have about the same power requirement as the audio section of the iPhone, i.e. not very much. There is no volume control associated with the iStreamer since it is not an amplifier (just a DAC), so the iStreamer's demand on the Mophie would be for the low-power DAC circuits plus additional power with which to charge the iPhone.
The total runtime for the iStreamer-iPhone combination powered by the Mophie battery was 4 hours and 40 minutes. At the beginning of this test my iPhone had a 70 percent charge which rose to 100 percent after about 75 minutes. From past experience with rechargeable devices, most of those systems charge very quickly in the first minutes or hours, then after the device's charge reaches a certain level the charging rate drops to what's called a "trickle" charge. That would mean that had my iPhone been completely discharged at the beginning of the test with the iStreamer, the total runtime would likely have been less, perhaps 30 to 40 minutes less. On the flipside, if my iPhone had a full charge at the beginning the total runtime may have been greater than 5 hours.
When the Mophie battery was completely discharged, I disconnected everything and plugged it into a 2.1 amp USB AC adapter for recharging. It took 6-1/2 hours to completely charge the Mophie, so if someone were going to use it or a similar battery to run audio gear in place of a USB AC adapter, I would recommend buying two such batteries, otherwise the music would stop at inconvenient times or the battery would have to be recharged much more frequently than what is ideal. Regardless of what the manufacturer states about how there are no battery-life penalties for topping off the battery frequently, the best long-term battery life is achieved with complete discharge and recharge cycles.
There would not be much point in running a test with audio gear as described if the Mophie didn't output a very steady current. In fact, since the point of using an external DAC with the iPhone is to get a slightly improved sound quality, and since the iStreamer does not contain a battery (i.e. it doesn't buffer any power that I know of), any slight power fluctuations from the Mophie would tend to abrogate the advantage of using the external DAC. I monitored the sound during the test to see whether there were any detectable glitches, warbles, "jitter", or any other artifacts that would negate the usefulness of this method of powering the iStreamer DAC. I didn't hear anything that would indicate a problem.
Lastly, the reason for using a battery such as the Mophie to power a DAC instead of powering the DAC from a USB AC mains adapter is to reduce or eliminate the effects of power fluctuations that occur when plugged into the AC mains. I don't know that Mophie or any other external battery manufacturer offers any assurance of rock-steady power with their batteries, since the purpose of those batteries is merely to charge iPhones and the like. It is however a long-established technique for getting smoother power into certain DC-powered audio devices, and that includes such top-quality and very expensive products as Nagra audio recorders used in the field.