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Taken from Fundamental of Physics 10th Edition

My question is "Why does the book's solution state that C1 and C2 are capacitors in parallel?

I understand two things:

  • The capacitors in parallel mean that the capacitors are directly wired together at one plate and directly wired together at the other plate, and that the same potential difference V is applied across the two groups of wired-together plates.

  • The capacitors in series mean that the capacitors are wired serially, one after the other, and that a potential difference V is applied across the two ends of the series.

The heart of this problem is that I have to find the equivalent capacitor. By finding the equivalent capacitor, it's basically a single capacitor that has the same capacitance as the combination of all the capacitors in a given circuit.

Applying those two bullet point concepts above, wouldn't C3 and C2 be capacitors connected in parallel?

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C1 and C2 are connected in parallel because they have one terminal connected together (at point "a"), and the other terminal connected together by the wires connecting points "b" and "c".

C2 and C3 are not connected in parallel because one of the terminals of C3 is connected to the battery and not to C2.

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  • $\begingroup$ So, in regards to capacitors C1 and C2, what you are saying is that the battery maintains potential difference V across the each of those capacitors? (And not C3 since you stated that C3's terminal is connected to the battery and not to C2) $\endgroup$ – 808poke Jan 9 '17 at 4:52
  • $\begingroup$ No, C3 keeps it from doing that. The battery applies a potential difference between the two nodes it's connected to. $\endgroup$ – The Photon Jan 9 '17 at 4:53
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By simply redrawing the circuit diagram, it is easier to understand and actually see why C1 and C2 capacitors are parallel: Circuit Diagram Redrawn

From the redrawn diagram, both terminals of C1 and C2 connect to each other. Compared to C1 and C2, C3 is not parallel due to the fact that its right terminal is connected to the battery, so that terminal does not directly reach one of the other capacitor's terminals.

The overall equivalent capacitance of this circuit diagram includes capacitors in series and in parallel. As a result, the equation for the equivalent capacitance is:

Ceq = [C3-1 + (C1 + C2)-1]-1

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