Final answer:
When a charged capacitor is connected to an uncharged one, the charge redistributes until both reach the same voltage. Capacitance is a property of the capacitors and does not depend on the presence of charge but on their physical attributes. Series connections decrease total capacitance, while parallel connections increase it.
Step-by-step explanation:
When one charged capacitor is connected to another uncharged capacitor, several things can happen. The initial charge on the charged capacitor will redistribute between the two capacitors until they both reach the same voltage. This happens because in a conductor, potential (voltage) must be constant, and so the charge will move until this condition is met. The total charge remains conserved during this process due to the conservation of charge.
The final charge on each capacitor depends on their individual capacitances. If both capacitors have the same capacitance, they will end up with equal charges. However, if their capacitances are different, the one with the higher capacitance will end up with a larger amount of charge. When capacitors are connected in series, the total capacitance of the circuit decreases, and this is calculated as the reciprocal of the sum of the reciprocals of each individual capacitor's capacitance. In a parallel connection, the capacitances simply add up to give the total capacitance.
Furthermore, the assertion that 'the value of the capacitance is zero if the plates are not charged' is false. Capacitance is a property of the capacitors themselves and does not depend on the presence of charge; it's defined by the physical attributes of the capacitor, such as the area of the plates and the distance between them.