Storage of capacitors in series

[LeakyFrog]

Homework Statement

Two identical capacitors that have been discharged are connected in series across the terminals of a 100V battery. When only on of the capacitors is connected across the terminals of the battery, the energy stored is U. what is the total energy stored in the two capacitors when the series combination is connected to the battery? a) 4U, B)2U, C)U D)U/2 E)U/4

Homework Equations

U = 1/2 CV²
1/C_eq = 1/C₁+1/C₂

The Attempt at a Solution

The only attempt I can think to make is to get U with one capacitor in terms of C1 and then get U2 in terms of C1 and C2 and then find the ratio of them. When I do this though I keep getting U/U2 = C2/(C1+C2) Which is not any of the answers. So I'm not really sure where to go from here.

 

[rl.bhat]

U/U2 = C2/(C1+C2)
In the problem, it is given that C1 = C2.
Ceq = C/2
U1 = 1/2CV^2
U2 1/2*C/2*V^2
So U1/U2 = ...?

 

[LeakyFrog]

How did you know that C1 = C2? With that bit of knowledge I got D) (U/2) as the answer. Thanks for your help.

 

[AdamP]

It says two identical capacitors.

 

[rdl]

I would approach this problem by first understanding the concept of capacitors in series. When capacitors are connected in series, their equivalent capacitance is given by 1/Ceq = 1/C1 + 1/C2. This means that the total capacitance of the series combination is less than the individual capacitances of the two capacitors.

Next, I would use the equation U = 1/2 CV^2 to calculate the energy stored in the individual capacitors when connected to the battery. Since the capacitors are identical, the energy stored in each capacitor would be the same, let's call it U1.

When the series combination is connected to the battery, the total energy stored would be the sum of the energies stored in the individual capacitors, which would be 2U1.

Therefore, the correct answer would be B) 2U. This makes sense because the equivalent capacitance of the series combination is half of the individual capacitance, which would result in twice the energy stored.

In summary, to find the total energy stored when capacitors are connected in series, we can use the equation U = 1/2 CV^2 and the concept of equivalent capacitance.