Question

A 7x10^-6F and 3x10^-6F capacitor are connected in series across a 24V battery? What voltage is required to charge a parallel combination of the two capacitors to the same total energy?

Answer 1

The voltage required is 11 V.

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First calculate the total capacitance of each combination.

Series: `C_S=1/(1/C_1+1/C_2)=1/(1/7+1/3)=2.1muF`

(Note that I did not convert the `muF` into `F` therefore my answer was in `muF`.)

Parallel: `C_P=C_1+C_2=7+3=2.1muF`

Next calculate the energy stored in the series arrangement:
`E_S=1/2C_SV_S^2=0.5×2.1×10^-6×24^2=6.05×10^-4J`

Now calculate the voltage that would give the parallel combination the same total energy stored (`E_P=E_S`):

`E_P=1/2C_PV_P^2 ⇒ V_P = sqrt((2E_P)/C_P) = sqrt((2×6.05×10^-4)/(10×10^-6))=11V`