# AP Physics 2 : Resistivity

## Example Questions

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### Example Question #1 : Resistivity

You have a 4cm long copper wire with a radius of 0.5mm. You have experimentally determined the resistance of the wire to be . What is the resistivity of copper?

None of the other answers is correct

Explanation:

The resistivity of a material is how much the material resists the flow of charge through it. Metals have low resistivities (which makes them good conductors), while things like glass or plastic have high resistivities.

The equation for resistivity is as follows:

is the length of the wire,  is the cross-sectional area,  is the resistance, and  is the resistivity. We have values for  and , and we're given the radius of the wire so we can find , so we're trying to solve for . If we rearrange the equation, we end up with this:

We're given the radius of the wire, so to find the area, we square the radius and multiply it by .

Now, we can plug in our values.

### Example Question #2 : Resistivity

You create a cylinder of an unknown material that has a diameter of , and a height of . You attach the electrodes to the faces of the cylinder and find the sample has a resistance of .

What is the resistivity of the material?

Explanation:

Use the equation for resistivity:

First, find the cross sectional area.

Plug in known values.

### Example Question #3 : Resistivity

You have a sample that is a cube of volume . You attach electrodes to opposite faces and find the resistance to be

What is the resistivity of the material?

Explanation:

Since we have a cube of volume , the length of the material must be . Use the equation for resistivity.

Rearrange the equation and plug in known values.

### Example Question #1 : Resistivity

You have a material with resistivity . You build a component of a fuel cell out of this material with a cross sectional area of  , and a thickness of .

What will be the resistance of this component?

None of these

Explanation:

Use the resistivity equation:

### Example Question #5 : Resistivity

You are researching new materials for usage in spacecraft electronics.

You have a new material, known as "Type F."

You carve out a cylinder of the material. It is  tall, with a radius of .

You put electrodes on each face of the cylinder.

You determine the resistance to be .

What is the resistivity of "Type F?"

None of these

Explanation:

We will use the relationship

Where  is the resistivity,  is the resistance,  is the surface area of the face the current is coming in or out of, and is the length from one face to the other.

Remember that the area of a circle is

Combining our equations we get

We then need to plug in our values

### Example Question #6 : Resistivity

You are researching new materials for usage in spacecraft electronics.

You have a new material, known as "Type G."

You carve out a cylinder of the material. It is  tall, with a radius of .

You put electrodes on each face of the cylinder.

You determine the resistance to be .

What is the resistivity of "Type G?"

None of these

Explanation:

We will use the relationship

Where  is the resistivity,  is the resistance,  is the surface area of the face the current is coming in or out of, and is the length from one face to the other.

Remember that the area of a circle is

Combining our equations we get

We then need to plug in our values

### Example Question #7 : Resistivity

You are researching new materials for usage in spacecraft electronics.

You have a new material, known as "Type Z."

You carve out a cylinder of the material. It is  tall, with a radius of .

You put electrodes on each face of the cylinder.

You determine the resistance to be .

What is the resistivity of "Type Z?"

None of these

Explanation:

We will use the relationship

Where  is the resistivity,  is the resistance,  is the surface area of the face the current is coming in or out of, and is the length from one face to the other.

Remember that the area of a circle is

Combining our equations we get

We then need to plug in our values

### Example Question #8 : Resistivity

A researcher is testing the electrical properties of a circuit that contains a resistor of unknown material. The resistor is a  cylinder with a radius of . The researcher measures the resistance of the resistor to be . What is the resistivity of this unknown material?

Explanation:

Use the equation for resistivity:

Here,  is the resistivity,  is the resistance,  is the cross-sectional area, and  is the length of the resistor.

Begin by finding the cross-sectional area of the material, which is circular:

Now plug in all known values and solve for resistivity.

### Example Question #9 : Resistivity

A scientist carves out a cylinder of a new material she developed. It is  tall, with a radius of . She put electrodes on each face of the cylinder. She determined the resistance to be . What is the resistivity of this material?

None of these

Explanation:

Use the relationship:

Here, is the resistivity,  is the resistance,  is cross sectional area, and  is the length.

The area of a circle is:

Substitute:

Plug in given values and solve

### Example Question #10 : Resistivity

There is a sample of an unknown material under testing. It is  tall, with a radius of . Electrodes are placed on each face of the cylinder. It is determined that the resistance to .

What is the resistivity?

None of these

Explanation:

Using the relationship

Where  is the resistivity,  is the resistance,  is the cross sectional area, and is the length from one face to the other.

The area of a circle is

Combining equations

Plugging in values

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