Two capacitors are in series, such as in this circuit diagram:


When doing a circuit analysis, how can we describe the voltages and charges across the two capacitors?


closed as off-topic by John Rennie, Yashas, hft, Feynmans Out for Grumpy Cat, Bill N May 14 at 13:46

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  • Charge: If you consider the inner plates of the two capacitors together with the wire that connects them, you get a single isolated conductor:

    Since there is essentially zero charge in the wire itself, and the conductor is neutral, you need the charges on the two plates to be opposite. This means that, under the most reasonable sign convention for how the capacitors are wired (i.e., with both the same way), the charges are equal: $$ Q_1=Q_2. $$

  • Voltage: The voltage is the line integral of the electric field, which takes a nonzero value in the spaces between the capacitor plates, and a negligible value within the wires.

    This means that voltage is additive over the capacitors: $$ V = V_1 + V_2. $$


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