Capacitors and Dielectrics of a circuit

In summary, the potential difference across the plates of the capacitor filled with a dielectric must be 2.7 V in order to store the same amount of electrical energy as the empty capacitor that is connected to a 6.0 V battery. The equation for capacitance of a parallel plate capacitor is C = epsilon * A / d, and the relationship between epsilon-zero and the epsilon inside the dielectric is that the dielectric constant (k) is equal to the ratio of epsilon to epsilon-zero.
  • #1
spoonthrower
37
0
Two capacitors are identical, except that one is empty and the other is filled with a dielectric ( k= 5.00). The empty capacitor is connected to a 6.0 V battery. What must be the potential difference across the plates of the capacitor filled with a dielectric such that it stores the same amount of electrical energy as the empty capacitor?

So here are my thoughts so far...
V= 6 V
Energy=.5CV^2
So the energy of the empty capacitor is .5V^2 which is .5(18^2)=18 right? they give no value for C so i assume it is one?
I have no idea where k comes into the picture. please help. thanks.
 
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  • #2
What is the equation for the capacitance of a parallel plate capacitor in terms of epsilon, A (area) and d (separation distance), ignoring fringe effects at the edges? What is the relationship between epsilon-zero (vacuum value) and the epsilon inside the dielectric?
 
  • #3
Answer

I just figured it out.
Energy=.5CV^2
Energy=.5kV^2

so .5CV^2=.5kV^2
so CV^2=kV^2
C=1
so V^2=kV^2
so 6^2=5V^2
so V= sqrt(36/5)=2.7 V
 

1. What is a capacitor and how does it work?

A capacitor is an electronic component that stores electric charge. It consists of two conductive plates separated by an insulating material, known as a dielectric. When a voltage is applied across the capacitor, it stores energy in the form of an electric field between the plates.

2. What is the purpose of a dielectric in a capacitor?

The dielectric in a capacitor serves to increase the capacitance, or the ability to store charge. It does this by reducing the electric field between the plates, allowing for a greater amount of charge to be stored on each plate. Different types of dielectrics have different permittivity values, which affect the capacitance of the capacitor.

3. How are capacitors and dielectrics used in circuits?

Capacitors are used in circuits for a variety of purposes, such as filtering, decoupling, and energy storage. They can also be used to block or pass certain frequencies of signals. The type of dielectric used in a capacitor can affect its performance in these applications.

4. What factors affect the capacitance of a capacitor?

The capacitance of a capacitor is affected by several factors, including the surface area of the plates, the distance between the plates, and the type of dielectric used. Generally, a larger surface area and smaller distance between plates will result in a higher capacitance. The permittivity and thickness of the dielectric also play a role in determining the capacitance.

5. How do dielectrics affect the breakdown voltage of a capacitor?

The breakdown voltage of a capacitor is the maximum voltage that can be applied before the dielectric material breaks down and allows current to flow through the capacitor. Different dielectrics have different breakdown voltage values, which can affect the overall performance and safety of the capacitor in a circuit. It is important to choose a dielectric with a high enough breakdown voltage for the desired application.

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