Which quantities are not the same for this capacitor setup?

In summary, when two parallel-plate capacitors with the same plate separation but different capacitance are connected in parallel to a battery and filled with air, the potential difference and electric field between the plates will remain the same. The dielectric constant will also remain the same. The only quantity that will not be the same for both capacitors when they are fully charged is the charge on the positive plate (D). This is because the capacitances are different, causing the total energy stored in each capacitor to be different.
  • #1
eprparadox
138
2

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?
 
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  • #2
eprparadox said:
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?
 
  • #3
@TSny U is the energy density.
 
  • #4
eprparadox said:
@TSny U is the energy density.
No. Check your textbook or class notes.
 
  • #5
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.
 
  • #6
No problem. Good work.
 

Related to Which quantities are not the same for this capacitor setup?

1. What is a capacitor?

A capacitor is an electronic component that stores electrical energy in an electric field. It consists of two conductive plates separated by an insulating material called a dielectric.

2. How does a capacitor work?

A capacitor works by accumulating and holding an electrical charge on its plates. When a voltage is applied to the capacitor, one plate becomes positively charged and the other becomes negatively charged. This creates an electric field between the plates, which allows the capacitor to store energy.

3. What quantities are not the same for this capacitor setup?

The quantities that are not the same for a capacitor setup are capacitance, voltage, and charge. The capacitance is determined by the physical characteristics of the capacitor, such as the size of the plates and the distance between them. The voltage across the capacitor and the amount of charge stored on the plates can vary depending on the circuit in which the capacitor is connected.

4. How does the capacitance affect the functioning of a capacitor?

The capacitance of a capacitor determines how much charge it can hold for a given voltage. A higher capacitance means that the capacitor can store more charge, while a lower capacitance means it can store less charge. It also affects the amount of time it takes for the capacitor to charge and discharge.

5. Can the capacitance of a capacitor be changed?

Yes, the capacitance of a capacitor can be changed by altering the physical characteristics of the capacitor, such as the distance between the plates or the type of dielectric material used. It can also be changed by connecting multiple capacitors in series or parallel in a circuit.

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