[Physics] Why is voltage added when batteries are connected in series but not in parallel

batterieselectric-circuitsvoltage

As I understand, the different voltage between two object is caused by the total different charged between two object. Thus, the higher extra electron between two opposite charged object, the higher voltage between them, isn't it? So if i have two battery or capacitor connect in parallel, the negative connect to negative, the positive connect to the positive. Caused the charge from each plate to be double. So that's as my expected, it must be double voltage, but ironically why it's out of my expected and the reality is vice-versa?

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Best Answer

You're reasoning from a faulty premise. The voltage difference depends on the strength of the electric field between the two points.

If and only if the electric field strength increases proportionally with the charge will your reasoning be correct.

But, in the two examples you give, this isn't the case.

For example, when you connect the two identical charged capacitors in parallel, the total plate area doubled so the surface charge density (total charge divided by total area) is unchanged and, thus, the electric field strength between the plates is unchanged.

Recall that, for a capacitor, the voltage across is proportional to

$$V \propto \frac{Qd}{A}$$

So if you double the charge $Q$ and double the plate area $A$, the voltage does not change

$$\frac{Qd}{A} = \frac{2Qd}{2A}$$

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