Why's Potential Difference Different in Series Capacitors?

In summary, the book states that in a series connection, the magnitude of charge on all plates is the same. However, the potential differences of individual capacitors are only equal if their capacitances are also equal. If all plates are the same size and have equal charge, their capacitances would be equal and thus the potential differences would also be equal. This aligns with the rule for total capacitance of two capacitors in series, where the potentials add and the magnitude of charges on the plates are the same. Additionally, it is important to note that capacitance is defined as the ratio of charge to voltage, and the charge on capacitors in series is always the same. This can be used to calculate the voltage across individual capacitors
  • #1
taco01
4
0
My book says "the magnitude of charge on all plates in a series connection is the same." It then says "potential differences of the individual capacitors are not the same unless their individual capacitances are the same." If the plates were all the same size, given that they all have equal charge, their capacitances would be the same, and therefore the potential differences of the individual capacitors would also be the same, right?
 
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  • #2
That seems to agree with what the book says — if the capacitance are the same, then the potential differences are the same.
 
  • #3
If you have two capacitances in series, the potentials add and the magnitude of the charges on the plates are all the same. Thus you have
$$U_1+U_2=U \; \Rightarrow \; Q \left (\frac{1}{C_1}+\frac{1}{C_2} \right)=\frac{Q}{C} \; \Rightarrow \; \frac{1}{C_1}+\frac{1}{C_2}=\frac{1}{C},$$
i.e., you get the rule for the total capacitance of two capacitors in series. Now indeed
$$U_1=\frac{C}{C_1} U = \frac{C_2}{C_1+C_2} U, \quad U_2=\frac{C}{C_2}U=\frac{C_1}{C_1+C_2} U.$$
 
  • #4
First understand that capacitance, C is defined as the ratio of charge, Q to voltage V.
C = Q / V
V = Q / C
Next understand that the charge Q, on capacitors in series is the same on each capacitor.

From that you can calculate the voltage across individual capacitors in series.
 

1. What is potential difference?

Potential difference, also known as voltage, is the difference in electric potential between two points in an electric circuit. It is measured in volts and is responsible for the flow of electric current.

2. How does a series circuit with capacitors differ from a parallel circuit?

In a series circuit, capacitors are connected one after the other, while in a parallel circuit they are connected side by side. This means that in a series circuit, the same amount of charge passes through each capacitor, while in a parallel circuit, the charge is split between the capacitors.

3. Why is potential difference different in series capacitors?

In series capacitors, the potential difference is different because the capacitors are connected in a chain, and the total potential difference is divided among them. This is known as voltage division, and it is a result of the capacitors storing and releasing charge in a sequential manner.

4. How does the capacitance affect the potential difference in series capacitors?

The capacitance of a capacitor is a measure of its ability to store charge. In series capacitors, the combined capacitance is less than the individual capacitance of each capacitor. This means that for the same amount of charge, the potential difference will be higher in series capacitors compared to a single capacitor.

5. Can the potential difference in series capacitors ever be equal?

No, the potential difference in series capacitors can never be equal. This is because the capacitors are connected in a chain, and the total potential difference is divided among them. Even if the capacitors have the same capacitance, the potential difference will still be different due to their sequential charging and discharging.

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