# Charges of capacitors in series and in parallel

• greg_rack
In summary, the conversation discusses the concept of charge conservation and how it relates to series and parallel capacitors. In series capacitors, the total charge is equal to the individual charges, while in parallel capacitors, the total charge is the sum of the individual charges. This is due to the fact that charge does not cross the capacitors and therefore must be conserved.
greg_rack
Gold Member

Very simply, I can't understand why the charges of capacitors placed in series are all the same, and why even the total one(of the circuit) is equal to those.
How is it possible that the total charge is the same as the individual ones?
There must be some concept/property about capacitors which I'm not getting.
On the other hand, for parallel capacitors, the total charge is the sum of those of the single capacitors, and that's what I would assume generally and logically.

Consider the wire connecting the two capacitors. Assuming it was not given some additional charge, the sum of the charges on the two connected plates must be zero.

Doc Al said:
Consider the wire connecting the two capacitors. Assuming it was not given some additional charge, the sum of the charges on the two connected plates must be zero.
Why? Couldn't they just bring the potential to zero by having the sum of ##\frac{q}{C}## ratios equal to the battery voltage??

greg_rack said:
Why?
Because charge is conserved. They start with zero charge and that just gets distributed between the connected plates.

greg_rack said:
Couldn't they just bring the potential to zero by having the sum of ##\frac{q}{C}## ratios equal to the battery voltage??
Not sure what you are saying here. The battery voltage equals the sum of the voltages across each capacitor.

davenn, etotheipi, vanhees71 and 1 other person
You should consider the total charge that moves to charge the capacitors.
In the series case the total charge that moves is ##Q=Q_1=Q_2## because first it moves through one capacitor and then the same(because they are in series) charge it moves through the second capacitor.
In the parallel case ##Q_1## charge moves through one branch and ##Q_2## charge moves through the other branch so the total charge that moves is ##Q=Q_1+Q_2##.

etotheipi, vanhees71, phinds and 1 other person
Another way of saying the same thing is this. Consider the "H" shaped conducting piece between the two capacitors. It is initially neutral and, because it is isolated from the battery, it remains neutral when the battery is hooked up. Thus the total negative charge on the left side of the H must be equal in magnitude to total positive charge on the right side. Since, by definition, the charge ##Q## on a capacitor is the absolute value on either one of its plates, the two capacitors must have the same charge. Note that no mention was made of the capacitance of each capacitor, therefore this result is true regardless of the capacitances; it's a result of charge conservation.

etotheipi, vanhees71, phinds and 1 other person
Yet another way of saying the same thing is to remember that the charge on a capacitor is given by ##q(t) = \int i(t) \ dt##. Since the capacitors are in series ##i(t)## is the same for all of them so ##q(t)## is also the same for all of them.

Simply put, charge conservation and the fact that charge does not cross the capacitor lead to this result.

etotheipi, vanhees71, greg_rack and 1 other person
Thanks guys, I got it!

kuruman, etotheipi, vanhees71 and 2 others

## 1. What is the total capacitance of capacitors in series?

The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of each individual capacitor's capacitance. In other words, if you have capacitors with capacitances C1, C2, C3, etc. in series, the total capacitance is equal to 1/C1 + 1/C2 + 1/C3 + ...

## 2. How are charges distributed in capacitors in series?

In capacitors in series, the charges are distributed equally among all the capacitors. This means that the charge on each capacitor is the same and the total charge on the series combination is equal to the sum of the charges on each individual capacitor.

## 3. What happens to the total voltage in capacitors in series?

The total voltage in capacitors in series is equal to the sum of the individual voltages across each capacitor. This means that the total voltage in a series combination is equal to the sum of the voltages across each individual capacitor.

## 4. How is the total capacitance of capacitors in parallel calculated?

The total capacitance of capacitors in parallel is equal to the sum of the individual capacitances. This means that if you have capacitors with capacitances C1, C2, C3, etc. in parallel, the total capacitance is equal to C1 + C2 + C3 + ...

## 5. What happens to the total charge in capacitors in parallel?

In capacitors in parallel, the total charge is equal to the sum of the charges on each individual capacitor. This means that the total charge in a parallel combination is equal to the sum of the charges on each individual capacitor.

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