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## Solar battery chargers

Recently, there are quite a lot of solar battery chargers. Such instruments like the one in the following image are able, in theory, to recharge mobile devices, ipods, etc when they are charged, and charge themselves using the sun light.

In this particular example, the company provides the following specifications for the instrument: it has a charge capacity of 3.5 Ah (Ampere  hour) at a potential difference of 3.7 Volts. That means it contains 12.95 Watt h energy when it is fully charged. Just for comparison, a small auto battery has like 40 A.h at a potential difference of 12 V.  That means the energy stored in the device is like 2% of the energy stored in an auto battery, so it is quite a bit actually.

Needless to say, you can charge it via AC adapter or USB cable of your laptop and use it to charge your mobile phone when required. The life cycle according to the webpage is 500. Indeed, the typical Lithium-ion polymer batteries have a life cycle of 1000 or more. Perhaps due to irregular solar charging rather than the standard net charging, the life cycle will be shorter as expressed in the webpage.

Can it really charge itself via solar radiation? I try to simply evaluate how much solar energy it can absorb, according to the data given in the webpage. The solar constant, the energy that the unit area on the top of the earth atmosphere receives in a second is about S = 1400 Watt per square meter. On tropical latitudes, the received energy on the ground is larger than 1000 W/m2. On middle latitudes like central Europe, and in a summer day, S = 800 W/m2. In winter, it is usually about 500 to 600 W/m2 in a sunny day. When it is overcast and very dark, it drops to values comparable to 1W/m2.

Now let us calculate how long it takes to collect 12.95 Wh energy from the received solar radiation on an average day. The collecting area, according to webpage, is 11.5 x 6.0 cm2 , and the efficiency is 17%. If I take S = 300 W/m2 for a relatively bright day, then the rate of collecting energy is

Area  x  Solar constant  x  efficiency = 69 cm2 x 300 W/m2 x 0.17 = 0.35 Watt.

Therefore to collect 12.95 Wh, i.e. to recharge the battery via sun light,  one has to keep the instrument in sunshine for 37 hours. In tropical regions, this time can be a factor 2 or 3 shorter.

This simple calculation shows that if you have such an instrument, you should be patient to get it charged using its own solar panel. In practice, the charging time can be longer because of the cloudy sky, and a decline of the efficiency with aging.

Do you save money if you buy it?

Perhaps not, specially if you live in high latitudes. The instrument can, in theory, work for 500 cycles of 12.95 Wh. That amounts to 6.5 kWh during its lifetime. The electricity price in expensive cases is like half a dollar per kWh. That means you collect in total like 3.2 US dollar while the instrument costs like 40+ dollars. This particular device is more a (big) spare battery than a solar charger.

There are better options. Consider a similar instrument with an area of 2-3 times larger. That efficiently reduce the recharging time. In addition, I guess the systems with rechargeable AA batteries have the ability to live longer: you can exchange those batteries when they are dead. The solar panels usually work much longer (like 10+ years).

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