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So let me get this straight...

Say you have 2 capacitors in series, with the combination of these two capacitors having a charge of 100C. Then each capacitor within the combination would have a charge of 100C?

And vice-versa, if you have 2 capacitors in parallel, and the combination of these two capacitors has a voltage of 100V, then each capacitor within the combination would have a voltage of 100V?

Why is this?

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If you have two capacitors in series as shown in the diagram below the plates $B$ and $C$ are electrically isolated from the outside world.
So if the net charge on the capacitors starts off as zero, then the net charge on those two plates will stay at zero.

Putting a charge on plate $A$ induces a charge of $-Q$ on plate $B$.
Since the net charge on $B$ and $C$ has to be zero there must be a charge of $+Q$ on plate $C$ which then indices a charge of $-Q$ on plate $D$.

enter image description here

With the capacitors configured as in the right hand diagram with potential differences $V_1$ abd $V_2$ across the capacitors connected the top two plates would cause a current to flow between the two plate (and the bottom two plates) until the potential difference actrss each capacitor was the same.

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  • When a battery is attached, electrons flow as far away from the negative terminal as possible. They end at the first plate of the first capacitor.
  • They repel exactly the same amount of electrons from the opposite plate (on the same capacitor), so there will be just as much negative charge on the first plate as there is positive charge on the other. This is induced charge.
  • The electrons running away from that second plate, tries to get as far away as possible. They end at the first plate of the second capacitor. This plate thus has exactly the same negative charge as the second plate (on the other capacitor) lost. All charges are equal just with different signs.
  • Again, the second plate on the second capacitor gets the exact same but positive charge because of repulsion.

Result: All plate on all series-connected capacitors have equal charge.

Voltage is the difference in electric potential $V$ (which is potential energy per charge). That depends on charge and distance:

$$V=k\frac Qr$$

Since the charges and distances are the same for both capacitors, $V$ is the same on both.

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    $\begingroup$ ...and concerning equal voltage on parallel capacitors....if it wasn't equal a current would flow until it is. $\endgroup$ – mikuszefski May 12 '17 at 6:40

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