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**HELP!!!A problem on electric energy storage**

**1. Homework Statement**

when two capacitors are connected in parallel and then connected to a battery, the total stored energy is 5.0 times greater than when they are connected in series and then connected to the same battery. What is the ratio of the two capacitances?(Before the battery is connected in each case, the capacitors are fully discharged)

**2. Homework Equations**

The equation for energy stored in a capacitor is U=1/2*(Q^2/C)

**3. The Attempt at a Solution**

The equation for capacitor connected in parallel wires: C=C1+C2

the equation for capacitor connected in series: C=(1/C1)+(1/C2)

The energy of capacitor connected in parallel is 1/2*(Q^2/C1)+1/2*(Q^2/C2)

the energy of capacitor connected in series is 1/2*(C1*Q^2)+1/2*(C2*Q^2)

Parallel energy/series energy=5

(1/2*(Q^2/C1)+1/2*(Q^2/C2))/(1/2*(C1*Q^2)+1/2*(C2*Q^2))=5

(Q^2/C)/(C*Q^2)=5

C=sqrt(1/5)=0.45

I am not really sure whether I did it correctly or not. Can I combine the energy of capacitor 1 with energy of capacitor 2?

Somebody please help me with it. thank you very much