# AP Physics 2 : Capacitors and Capacitance

## Example Questions

### Example Question #1 : Capacitors And Capacitance

Consider the circuit:

What is the total equivalent capacitance?

Explanation:

Equivalent capacitance in parallel is calculated by taking the sum of each individual capacitor. We can reduce the two parallel capacitors as the following:

The new equivalent circuit has two capacitors in series. This requires us to sum the reciprocals to find equivalent capacitance:

### Example Question #1 : Capacitors And Capacitance

You have 3 capacitors in series. Their capcitance's are , and . What is the total capacitance of the system?

None of the other answers is correct

Explanation:

To find the total capacitance of capacitors in series, you use the following equation:

.

Our values for , , and  are 4, 3, and 2. Now, we can plug in our values to find the answer.

The answer we have is the inverse of this. Therefore, the total capacitance is .

### Example Question #1 : Capacitors And Capacitance

You have 4 capacitors, , , , and , arranged as shown in the diagram below.

Their capacitances are as follows:

What is the total capacitance of the circuit?

Explanation:

Remember, the equations for adding capacitances are as follows:

Capacitors  and  are in series,  and  are in parallel, and  and  are in parallel.

### Example Question #101 : Circuits

In this parallel-plate capacitor, the distance  between the plates is , the area of each plate is , and the voltage across them is .

Calculate the capacitance.

Explanation:

The key hint to remember here is that the capacitance depends only on the geometry of the material, not the potential difference or electric field.

For a parallel-plate capacitor,

Plugging in the numbers given results in

Be careful to convert the units to meters!

### Example Question #1 : Capacitors And Capacitance

Three capacitors are in parallel with each other. What can be said for certain about the total capacitance?

The total capacitance is greater than any of the individual capacitances.

The total capacitance is the arithmetic mean of the individual capacitances.

The total capacitance is less than any of the individual capacitances.

The total capacitance is somewhere between the highest capacitance and the lowest capacitance (inclusive).

Nothing can be said for certain about the total capacitance.

The total capacitance is greater than any of the individual capacitances.

Explanation:

Capacitors in parallel combine according to the following equation:

.

Because the capacitances are additive, and all of the capacitances are greater than zero, no matter what numbers you use, you will always end up with a number that is greater than any of the individual numbers.

### Example Question #1 : Capacitors And Capacitance

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.

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 #921 : Ap Physics 2

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

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?

Stay the same

Decrease

It depends on the voltage of the battery

Increase

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?

Decrease

The charge is zero

Increase

Stays constant

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 #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 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?

Decrease

Stays constant

We need to know the capacitance of the capacitor

Increase