Capacitor question

I would like to verify my understanding of super capacitors and i will give a practical example that i found online a few days ago. It was regarding a cheap spot welder with small lipo battery. It was said that the design is not good and it would be better to include a super capacitor to aid the small battery. So it made me think whether i understand how capacitors in combination with a battery actualy work. In the attached image there are 3 examples and i would kindly ask you to check if my understanding of it is correct. Thanks

 
Adding a cap in parellel to the supply voltage is common, but depends on the circuits "thurstyness" for electricity.

What you intend is different. You want two dedundent power sources?
 
The thing about capacitors is that both the charging cycle and the discharge cycle are exponential. They are NOT linear.
There are two conclusions you can draw from this bit of information:
  1. You can NEVER charge the capacitor to be equal to the battery voltage. It can get arbitrarily close in a finite amount of time but will take an infinite amount of time to be equal to the battery voltage.
  2. You can NEVER discharge a capacitor all the way to zero voltage in a finite amount of time. It can however get small enough that it is difficult to measure.
It is legitimate to have different resistors that control the actual charging and discharging times of the capacitor. If you are interested in pursuing this, I can show you the equations for charging and discharging a capacitor with different resistors.
 
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