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Two or more capacitors are said to be connected in parallel if each one of them is connected across the same two points. In a parallel combination of capacitors potential difference across each capacitor is same but each capacitor will store different charge. Why is this true? Why is the potential difference across each capacitor in parallel the same and why will each capacitor store different charge?

Also, in series, why are Potential difference across each capacitor different, while charge is the same?

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  • $\begingroup$ Your title asks about capacitors in series (and is based on a false premise), but the main part of your question asks about capacitors in parallel. $\endgroup$ – The Photon Nov 10 '15 at 4:45
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Why are potential differences equal across two capacitors in series, but charge on each capacitor is not?

This is based on a false premise. There is no rule that says that "potential differences are equal across two capacitors in series".

In a parallel combination of capacitors potential difference across each capacitor is same but each capacitor will store different charge. Why is this true?

In a lumped circuit model, any two devices in parallel must have the same potential across them. This is because of Kirchoff's voltage law (KVL) which says that the net potential drop around any loop in a planar circuit is zero. To put it in more basic terms, if the potential at point 'A' is $V_a$ and the potential at point 'B' is $V_b$, then the potential difference between points A and B is $V_a - V_b$ no matter what path you take through the circuit between those points.

As arvindpujari's answer points out, since the potential differences are equal across the two parallel capacitors, this means that if the capacitance values aren't equal then they must have different charges since a linear capacitor is defined by the equation $V=Q/C$.

Also, in series, why are Potential difference across each capacitor different, while charge is the same?

Imagine you start with two capacitors in series with no charge ($V=0$). Then start driving a current through them. The same current will flow through both capacitors (that's what it means for two elements to be in series), so the same charge will accumulate on each capacitor's plates.

Since they have equal charge, if the capacitance values are not the same, then the potentials must also not be the same.

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For Capacitors, the charge stored in it is directly proportional to the potential difference across it. Hence, the charge stored in the capacitor is given by the relation $$Q=CV$$ where C is a constant known as capacitance which is an inherent property of the capacitor. In a parallel combination, the charge through each capacitor has the same entry and exit point, hence the potential difference across each capacitor will be the potential of exit point minus potential of entry point which is the same for both. Hence the potential difference across each capacitor is the same, and if the capacitance are different, naturally the charge stored in each will be different. In a series combination, since the charge stored is the same as the same charge flows through all the capacitors, the potential difference across each will be different.

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