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?

1 Answer
Jun 10, 2014

The voltage required is 11 V.


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#