Which quantities are not the same for this capacitor setup?

[eprparadox]

Homework Statement

Two parallel-plate capacitors with the same plate separation but different capacitance are connected in parallel to a battery. Both capacitors are filled with air. The quantity that is NOT the same for both capacitors when they are fully charged is:

A. potential difference
B. energy density
C. electric field between the plates
D. charge on the positive plate
E. dielectric constant

Homework Equations

$C = \frac{Q}{V}$

$C = \frac{\epsilon_0 A}{d}$

$U = \frac{1}{2}CV^2 = \frac{Q^2}{2C}$

The Attempt at a Solution

The answer is listed as D.

Because the capacitors are hooked up in parallel and stay connected to the battery, I know the potential difference (A) will remain the same (The electric field will also then remain the same (C)).

Dielectric constant is the same (E).

So it's between B and D.

We're told the capacitances are different and know that $U = \frac{1}{2}CV^2$.

If the capacitances are different, then it seems that the energy densities should also be different. But I also think the charge on each capacitor should be different. So I think both B and D won't the same!

Any thoughts on where I'm going wrong?

 

[TSny]

We're told the capacitances are different and know that $U = \frac{1}{2}CV^2$.

Is U the total energy stored in the capacitor or is it the energy density of the capacitor?

 

[eprparadox]

@TSny U is the energy density.

 

[TSny]

@TSny U is the energy density.

No. Check your textbook or class notes.

 

[eprparadox]

shoot, my bad. The energy density is a function of the electric field, which stays the same. This is the total energy. sorry about that.

 

[TSny]

No problem. Good work.