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You could not use lightning instead of batteries.
In general, no. You need to use the correct capacitor as designed for the circuit.
ceramic capacitor does not simultaneously discharges instead it maintains stead flow of charges through it
Batteries and capacitors serve quite different purposes and are usually not interchangeable.
If you use a lot of batteries, the long term benefit could be very good. If not, you need to weigh the cost because rechargeable batteries are very expensive and can take a while to recoup your investment.
You can always use a higher voltage rated capacitor, it will probably just last a little longer.
No
No. The purpose of the zener diode is to clip (turn on) at a certain voltage. A capacitor will not exhibit this behavior.
Yes. You can use a battery to charge a capacitor, which is an electrical device that stores static charge.
It allows you to use mains power instead of batteries
We could use leather instead.
Dry cells and automobile batteries require a medium in order to transmit and receive the signals from outer space.