HELP A problem on electric energy storage

[Kudo Shinichi]

HELP!A problem on electric energy storage

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)

Homework Equations

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

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

 

[Delphi51]

I don't know if this will help, but I hope it will get you started.
You must write an expression for the energy in the series circuit and another expression for the energy in the parallel circuit. Both will have V, C1 and C2 in them. Pesonally I always use E = 1/2*C*V^2 rather than that one with a Q in it.

Then you write that the parallel energy = 5*series energy.
Play with the resulting expression and see if you can solve it. No doubt it will be easier if you can divide by something to get rid of all individual C1 and C2 variables and only have the one variable C1/C2 which you can call x. It will look much easier when you have an equation involving x, which you are used to working with.

 

[Kudo Shinichi]

I don't know if this will help, but I hope it will get you started.
You must write an expression for the energy in the series circuit and another expression for the energy in the parallel circuit. Both will have V, C1 and C2 in them. Pesonally I always use E = 1/2*C*V^2 rather than that one with a Q in it.

Then you write that the parallel energy = 5*series energy.
Play with the resulting expression and see if you can solve it. No doubt it will be easier if you can divide by something to get rid of all individual C1 and C2 variables and only have the one variable C1/C2 which you can call x. It will look much easier when you have an equation involving x, which you are used to working with.

Buthow can I get rid of V? V is also an unknown variable for this question.
1/2*C1*V^2+1/2*C2*V^2=5*(1/2*1/C1*V^2+1/2*1/C2*V^2)
so do I use this to solve for the ratio?

 

[Delphi51]

There appears to be something wrong on the right side for the series capacitance.
This "C=(1/C1)+(1/C2) " that you used is not correct - it should be
1/C=(1/C1)+(1/C2) or C = (C1*C2)/(C1 + C2)

Divide both sides by V^2 and it is gone!

 

[Kudo Shinichi]

1/2*C1*V^2+1/2*C2*V^2=5*(1/2*(C1*C2)/(C1 + C2)*V^2)
Divide both sides by V^2
1/2C1+1/2C2=5/2((C1*C2)/(C1 + C2))
½(C1+C2)^2=5/2(C1*C2)
(C1+C2)^2=5(C1*C2)
C1^2+2C1*C2+C2^2=5C1*C2
C1^2-3C1C2+C2^2=0
Then use the quadratic equation to find out C right?