Suppose that three identical capacitors are connected to a battery. Will they store more energy if connected in series or in parallel?

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Suppose that three identical capacitors are connected to a battery. Will they store more energy if connected in series or in parallel?

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Answer 1 · 2018-04-24T08:41:36

Explanation:

Parallel

Combined capacitance:

$C_{T} = 3 C$ $C_T = 3C$

Stored energy:

$U_{p a r a l l e l} = \frac{1}{2} C_{T} V_{o}^{2} = \frac{3}{2} C V_{o}^{2}$ $U_( parall\el ) = 1/2 C_T V_o^2 = 3/2 C V_o^2$

Series

Combined capacitance:

$\frac{1}{C_{T}} = \frac{3}{C} \Rightarrow C_{T} = \frac{C}{3}$ $1/C_T = 3/C implies C_T = C/3$

Stored energy:

$U_{s e r i e s} = \frac{1}{2} C_{T} V_{o}^{2} = \frac{1}{6} C V_{o}^{2}$ $U_(series) = 1/2 C_T V_o^2 = 1/6 C V_o^2$

$\Rightarrow \frac{U_{p a r a l l e l}}{U_{s e r i e s}} = \frac{\frac{3}{2} C V_{o}^{2}}{\frac{1}{6} C V_{o}^{2}} = 9$ $implies U_( parall\el )/U_(series) = (3/2 C V_o^2)/(1/6 C V_o^2) = 9$

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Suppose that three identical capacitors are connected to a battery. Will they store more energy if connected in series or in parallel?

1 Answer

Explanation:

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