Final answer:
No, we cannot give any desired charge to a capacitor as the charge it can store is determined by its capacitance and the voltage applied. Adding a dielectric to a capacitor connected to a battery increases its capacitance.
Step-by-step explanation:
Can we give any desired charge to a capacitor? The answer to this question is No. A capacitor can only store as much charge as its capacitance and the voltage applied to it will allow. According to the relationship Q = CV, where Q is the charge, C is the capacitance, and V is the voltage, the charge stored is proportional to the capacitance and the voltage. Different capacitors will store different amounts of charge for the same applied voltage, depending on their physical characteristics.
Inserting a dielectric into a charged capacitor while it remains connected to a battery will increase their capacitance. The capacitance of a spherical capacitor does not depend on which sphere is charged positively or negatively. The assertion that the value of capacitance is zero if the plates are not charged is false; an uncharged capacitor still has a capacitance value, it just does not have any charge stored at that moment. When a capacitor has plates with different areas and is connected across a battery, the charges on each plate will not be the same due to the disparity in the areas.