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I have read the theory of capacitors and the equations and all. But I have some doubts.

  1. If I'm connecting one plate of a non polarity capacitor to positive of a battery and other plate to ground(negative of battery is connected to ground). How will the capacitor charges?

GND--(-cell+) --| |-- GND. Does a $+q$ charge accumalate on one side and other plate at $-q$ ? Will $-q$ get accumalated on the other plate as it is connected to ground.?

  1. Similar question, in CMOS circuits, there is the load capacitance, in which one end is at the output node and other end is grounded. So for the output to become one, the capacitor needs to get charged. In that case, the $+q$ charge will be accumalated on the output end plate , and what will happen to the other plate which is connected to ground ?
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Think from first principles about the movement of electrons near the capacitor plates.

On the diagram you posted, electrons on the left capacitor plate would leave and be attracted towards the positive side of the cell. This leaves the left capacitor plate positive. Since that one is positive, electrons would be attracted to the right capacitor plate (from within the wire on the right of the right plate) making the right one negative (the plates are very close together).

In this way the capacitor becomes charged even though no current can flow through it.

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