AP Physics 2 : Circuits

Study concepts, example questions & explanations for AP Physics 2

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Example Questions

Example Question #1 : Capacitors And Capacitance

Exam1 caps

Four arrangements of capacitors are pictured. Each has an equivalent capacitance. Rank these four arrangements from highest equivalent capacitance to lowest. Assume that all capacitors are identical.

Possible Answers:

Correct answer:

Explanation:

Let's go through all of them and find the equivalent capacitance.

(A) This is just 

(B) There are two capacitors in series, so this is 

(C) These capacitors are in parallel, so

(D) These are a combination of series and parallel.  Two are in series and they are in parallel with a third,

So, ranking them we get

Example Question #1 : Capacitors And Capacitance

If the maximum amount of charge held by a capacitor at a voltage of 12V is 36C, what is the capacitance of this capacitor?

Possible Answers:

Correct answer:

Explanation:

In this question, we're told the maximum amount of charge that a capacitor can hold at a given voltage. We're then asked to determine the capacitance. To do this, we'll need to use the expression for capacitance.

Plug in the values given to us in the question stem:

Example Question #1 : Capacitors And Capacitance

Imagine a capacitor with a magnitude of charge Q on either plate. This capacitor has area A, separation distance D, and is connected to a battery of voltage V. If some external agent pulls the capacitor apart such that D doubles, did the voltage difference between the plates increase, decrease or stay the same?

Possible Answers:

Stay the same

It depends on the voltage of the battery

Increase

Decrease

Correct answer:

Stay the same

Explanation:

The fact that the system is still connected to the battery indicate a constant V so regardless what happens to the capacitor, V stays fixed.

Example Question #1 : Capacitors And Capacitance

 

 

Imagine a capacitor with a magnitude of charge Q on either plate. This capacitor has area A, separation distance D, and is connected to a battery of voltage V. If some external agent pulls the capacitor apart such that D doubles, did the charge on each plate increase, decrease or stay the same?

Possible Answers:

Increase

Stays constant

Decrease

The charge is zero

Correct answer:

Decrease

Explanation:

Relevant equations:

Plug the second equation into the first:

Considering all the variables in the numerator are held fixed for this problem, we see that increasing D will decrease the charge stored on each plate. 

Example Question #281 : Electricity And Magnetism

Imagine a capacitor with a magnitude of charge Q on either plate. This capacitor has area A, separation distance D, and is not connected to a battery of voltage V. If some external agent pulls the capacitor apart such that D doubles, did the charge on each plate increase, decrease or stay the same?

Possible Answers:

Stays constant

Decrease

Increase

We need to know the capacitance of the capacitor

Correct answer:

Stays constant

Explanation:

The charge has no where to go. Without the battery connected, the charge has no physical avenue on or off the plates. 

Example Question #111 : Circuits

Imagine a capacitor with a magnitude of charge Q on either plate. This capacitor has area A, separation distance D, and is connected to a battery of voltage V. If some external agent pulls the capacitor apart such that D doubles, how did the capacitance change? Also, do we need to use the information provided about the battery?

Possible Answers:

Decrease, yes

Increase, no

Increase, yes

Decrease, no

Correct answer:

Decrease, no

Explanation:

As D increases, C will decrease

Does the battery matter? No. Capacitance is a "geometric" quantity. This means that it can be determined solely by physical parameters like the area and separation distance. The charge on the plates, voltage difference, electric field and any other quantity you could think of does not influence the capacitance other than A or D. 

Example Question #12 : Capacitors And Capacitance

Lazy capacitor

Consider the given diagram. If , each plate of the capacitor has surface area , and the plates are 0.1mm apart, determine the number of excess electrons on the negative plate.

Possible Answers:

None of these

Correct answer:

Explanation:

The voltage rise through the source must be the same as the drop through the capacitor.

The voltage drop across the capacitor is the equal to the electric field multiplied by the distance.

Combine equations and find the electric field:

Convert mm to m and plugg in values:

Use the electric field in a capacitor equation:

Convert  to  and plug in values:

The magnitude of total charge on the positive plate is equal to the total charge on the negative plate, so to find the number of excess elections:

Example Question #112 : Circuits

Lazy capacitor 

Consider the given diagram. If , each plate of the capacitor has surface area , and the plates at  apart, determine the excess charge on the positive plate.

Possible Answers:

Correct answer:

Explanation:

The voltage rise through the source must be the same as the drop through the capacitor.

The voltage drop across the capacitor is the equal to the electric field multiplied by the distance.

Combine equations and solve for the electric field:

Convert mm to m and plug in values:

Using the electric field in a capacitor equation:

Rearrange to solve for the charge:

Convert  to  and plug in values:

Example Question #11 : Circuit Components

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

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

What is the voltage difference across the capacitor? 

Possible Answers:

Correct answer:

Explanation:

Voltage difference  is given by

, where  is the electric field strength and  is the distance between the two plates. 

For this problem,

Example Question #15 : Circuit Components

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

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

Determine the capacitance of this system given that the space in between is a vacuum, and that the permittivity of empty space  is 

Possible Answers:

Correct answer:

Explanation:

The formula for capacitance  is given by:

,

Where  is dielectric strength,  is distance between plates,  is permittivity of empty space, and  is cross sectional area. 

To determine , we do

 because between the plates is a vacuum.

Putting it all together,

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