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B Why's Potential Difference Different in Series Capacitors?

  1. Feb 21, 2017 #1
    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?
  2. jcsd
  3. Feb 21, 2017 #2


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    That seems to agree with what the book says — if the capacitance are the same, then the potential differences are the same.
  4. Feb 22, 2017 #3


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    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
    $$U_1=\frac{C}{C_1} U = \frac{C_2}{C_1+C_2} U, \quad U_2=\frac{C}{C_2}U=\frac{C_1}{C_1+C_2} U.$$
  5. Feb 23, 2017 #4


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    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.
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