(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A complete circuit with a battery U = 12 V, and two capacitors in series, C1 = 10 microF, C2 = 20 microF. How much energy is stored in C1?

2. Relevant equations

[tex](1) W_c = 1/2 CV^2[/tex]

[tex](2) W_c = 1/2 Q^2/C[/tex]

[tex](3) C = Q/V[/tex]

[tex](4) C = 1/(C_1^{-1} + C_2^{-1})[/tex]

3. The attempt at a solution

I tried to use equation (1) above with C=C1. I was thinking that the potential over each capacitor is 12 V, so I used V=12 V in equation (1). And I was supposing that the battery had already charged the capacitors, so they were fully charged. My W_c (=72 microjoule) then is not the same as in the key (=320 microjoule).

In the key, the solution starts with finding the substituted capacitor for the circuit, according to equation (4). Then they get Q from equation (3), to get the total charge in the substituted capacitor. And then, they use equation (2) with C=C1 to get W_c.

4. Questions

a) Why isn't my method working?

b) Isn't the voltage over each capacitor also 12 V?

c) How can equation (2) be used as they do, with C=C1? That equation should only apply for C (the substituted capacitor), because Q in that equation applies for the substituted capacitor, and not for C1. Or why could it apply to C1, when Q is the charge for the substituted capacitor and not for C1?

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# Energy in capacitor

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