AP Physics 2 : Properties of Capacitors and Dielectrics
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Example Questions
Example Question #291 : Electricity And Magnetism
Fill in the blanks.
Dielectrics __________ capacitance because capacitance is __________ related to electric field strength, and dielectrics __________ effective electric field strength.
decrease . . . inversely . . . increase
increase . . . inversely . . . increase
increase . . . directly . . . increase
decrease . . . directly . . . decrease
increase . . . inversely . . . reduce
increase . . . inversely . . . reduce
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 #292 : Electricity And Magnetism
Two parallel conducting plates separated by a distance 
The electric charge on the plates is halved
The potential difference between the plates is doubled
The capacitance is unchanged
The electric charge on the plates is doubled
The potential difference between the plates is halved
The electric charge on the plates is halved
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 
Example Question #293 : Electricity And Magnetism
Capacitances are as follows:
What is the total capacitance of the system in the diagram above?
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 #294 : Electricity And Magnetism
Capacitances are as follows:
Consider the diagram above. If the battery has a potential difference of 
There is not enough information to find the energy of the system
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 
Example Question #295 : Electricity And Magnetism
A dielectric is put between the plates of an isolated charged parallel plate capacitor. Which of the following statements is true?
The capacitance decreases
The potential difference decreases
The potential difference increases
The charge on the plates decreases
The charge on the plates increases
The potential difference decreases
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 
Example Question #6 : Properties Of Capacitors And Dielectrics
Suppose I have a uniform electric field within a parallel plate capacitor.
Suppose the capacitor's plates are 
Given that the capacitance is 
To determine this, we can use the formula:
Where 
Solving for 
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