# AP Physics 2 : Properties of Capacitors and Dielectrics

## Example Questions

### Example Question #1 : Properties Of Capacitors And Dielectrics

Fill in the blanks.

Dielectrics __________ capacitance because capacitance is __________ related to electric field strength, and dielectrics __________ effective electric field strength.

decrease . . . directly . . . decrease

increase . . . inversely . . . reduce

decrease . . . inversely . . . increase

increase . . . directly . . . increase

increase . . . inversely . . . increase

increase . . . inversely . . . reduce

Explanation:

The reason dielectrics reduce the effective electric field strength is because when a dielectric is added, the medium gets polarized, which produces an electric field in opposition of the existing electric field.

When the electric field decreases, the capacitance increases because the plates are able to store more charge for the same amount of voltage applied, because there's less force repelling electrons from gathering on the plate.

### Example Question #2 : Properties Of Capacitors And Dielectrics

Two parallel conducting plates separated by a distance  are connected to a battery with voltage . If the distance between them is doubled and the battery stays connected, which of the following statements are correct?

The potential difference between the plates is halved

The capacitance is unchanged

The electric charge on the plates is doubled

The potential difference between the plates is doubled

The electric charge on the plates is halved

The electric charge on the plates is halved

Explanation:

The equation for capacitance of parallel conducting plates is:

When the distance is doubled, the capacitance changes to:

The battery is still connected to the plates, the potential difference is unchanged. Because , and the capacitance is halved while the voltage stays the same,  must necessarily drop to half to account for the change.

### Example Question #2 : Properties Of Capacitors And Dielectrics

Capacitances are as follows:

What is the total capacitance of the system in the diagram above?

Explanation:

Recall the equations used for adding capacitors:

From the diagram, capacitors A and B are in parallel, and capacitors C and D are in parallel, and those two systems are in series.

Use the equation above to find the equivalent capacitance of capacitors A and B.

Use the equation above to find the equivalent capacitance of capacitors C and D.

Use the equation above to find the total capacitance by adding the two systems of capacitors, which are in series.

Therefore, the total capacitance is

### Example Question #4 : Properties Of Capacitors And Dielectrics

Capacitances are as follows:

Consider the diagram above. If the battery has a potential difference of , what is the total energy of the system once it's fully charged?

There is not enough information to find the energy of the system

Explanation:

The equations for adding capacitors are:

To find the total energy, we need to know the total capacitance. To do that, we the capacitors together according to the rules above.

Capacitors A and B are in parallel.

Capacitors C and D are in parallel.

Add the systems of capacitors together. They are in series.

The total capacitance is

The equation for finding the energy of a capacitor is:

Plug in known values and solve.

Therefore, the system, when fully charged, holds  of energy.

### Example Question #3 : Properties Of Capacitors And Dielectrics

A dielectric is put between the plates of an isolated charged parallel plate capacitor. Which of the following statements is true?

The charge on the plates increases

The potential difference increases

The charge on the plates decreases

The potential difference decreases

The capacitance decreases

The potential difference decreases

Explanation:

When a dielectric is added to a capacitor, the capacitance increases. In our problem, it says the system is charged and isolated, which means no charge will escape the system. Therefore the charge on the plates will stay the same.

The equation for capacitance is:

Since the charge stays the same, and the capacitance increases, the potential difference must decrease so that  may increase.

### Example Question #4 : Properties Of Capacitors And Dielectrics

Suppose I have a uniform electric field within a parallel plate capacitor.

Suppose the capacitor's plates are  in length and  in width, and the space between the plates is

Given that the capacitance is , at what voltage difference is required for the capacitor to store  of charge?

Explanation:

To determine this, we can use the formula:

Where  is charge stored,  is voltage difference across a capacitor, and  is capacitance.

Solving for ,