Question

Electricity is generated in power stations in Watts (W). This must be stored in a battery first before getting supplied (in solar energy, for example). So, in the battery module, why is the power stored is in the units mAh (milli-ampere hour)? How does the two unit Watts (W) and mAh are connected to each other?

Also, why does the charger shows that: Input: 100-240V--2.5A 50-60 Hz and Output: 19.5V--6.7A (for example) and not the power supplied to the device's battery? (Which can, of course, be calculated by the formulae P=VI, which is both different at the input and output.

Answer 1

Electricity is generated in power stations, that's right. You can say POWER is generated at the power station, you cant say "electricity generated in power station in watts". Watts (W) is just the unit of power.

The second statement is wrong. For power transmission from the powerhouse, it does not required to store in battery also, it doesn't use any battery for supply. We get power directly from powerhouse using transmission lines. The power we received at any instant is generated at the same time at the power station (Electricity travelles with 1/100 th the speed of light.).

For solar energy, the case is different. For example, consider you have a 12V, 10A solar panel. you cannot use this directly with the electrical appliances. Because in India, the electrical devices are operating at 230V. So the technique we use is, First Charge a 12V,8A battery using the solar panel. then convert the 12V output of battery to 230V. The power stored in the battery is P=V*I=12*8=96W .
Now using some circuits and step-up transformer we convert the 12V output to 230V. NOTE: The power will be same even if we convert the voltage to 230V.
Besides, if you have a solar panel which produces 230V and enough power, you can directly use it with electrical devices without any battery. It is not practical too. Because Sunlight will not be available all the time.

Power is always measured in Watts(W). A milliampere-hour (mAh) is 1000th of an ampere-hour ( Ah ). Both measures are commonly used to describe the energy charge that a battery will hold and how long a device will run before the battery needs recharging.The symbol "mAh"—note the capitalization—means "milliampere-hour." This is a unit of electric charge, and it's the most common way to express the capacity of small batteries. (Bigger batteries are labeled in ampere-hours; 1 Ah = 1000 mAh.) You can calculate the capacity of a battery by multiplying the discharge current by the duration of time that the battery can supply that much current.Very roughly, a 1000 mAh battery can supply 1000 mA for one hour, or 100 mA for ten hours, or 10 mA for 100 hours, but this is a simplification since the capacity of the battery depends on the discharge rate. (How much it changes depends on the type of battery.) So a rating of 1000 mAh is actually an incomplete description of the battery's capacity unless you also know the corresponding discharge rate.

In India, the electricity is provided at 230V, Frequency is 50-55Hz. The current drawn by a device depends upon the resistance of that device. So Input: 100-240V--2.5A 50-60 Hz means, this device can work fine at a voltage of 100-240V, 50-60Hz frequency, and it may draw a maximum of 2.5A current.
You said the output shown is Output: 19.5V--6.7A. Ofcourse the power at the output is lesser than input.
This is because, the power provided from electric lines are very very high. For single phase connections, we are provided a power maximum of upto 2500 to 3000W. But we dont need that much power . So we use this kind of adapters to reduce the output voltage as well as the power. Otherwise the device may damage.