AP Physics 2 - Resistivity

A cylinder of an unknown material is being tested. It is tall, with a radius of . Electrodes are placed on each face of the cylinder. It is determined that the resistance is . What is the resistivity?

$.291\Omega*meters$

None of these

$.375 \Omega*meters$

$.931\Omega*meters$

$.762 \Omega*meters$

Explanation

Using the relationship

$\rho=R\frac{A}{l}$

Where $\rho$ 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

$A=\pi*r^2$

Combining equations:

$\rho=R\frac{\pi*r^2}{l}$

Plugging in values

$\rho=59\frac{\pi*.0095^2}{.0575}$

$\rho=.291\Omega*meters$

A resistor has cross sectional area $16\textup{ mm}^2$ and length $2\textup{ cm}$ . When placed in series with a $3\textup{ V}$ battery, a current of $56.0\textup{ mA}$ is produced. Determine the resistivity.

$\rho=1.764*10^{-3}\ \Omega\cdot \textup{m}$

None of the above

$\rho=2.028*10^{-3}\ \Omega\cdot \textup{m}$

$\rho=1.213*10^{-3}\ \Omega\cdot \textup{m}$

$\rho=3.751*10^{-3}\ \Omega\cdot \textup{m}$

Explanation

Using Ohm's law:

Converting to and plugging in values

Solving for resistance:

$R=8.82\Omega$

Using the equation for resistivity:

$\rho=R\frac{A}{l}$

Converting to and to and plugging in values:

$\rho=8.82\frac{2*10^{-6}}{.01}$

$\rho=1.764*10^{-3}\Omega*m$

A sample of a new material is being tested. It is tall, with a radius of . Electrodes are placec on each face of the cylinder. The resistance is determined to be .

What is the resistivity of this material?

$1.61*10^{-3}\Omega*meters$

None of these

$1.42*10^{-3}\Omega*meters$

$3.49*10^{-3}\Omega*meters$

$2.22*10^{-3}\Omega*meters$

Explanation

Using the relationship

$\rho=R\frac{A}{l}$

Where $\rho$ 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

$A=\pi*r^2$

Combining equations

$\rho=R\frac{\pi*r^2}{l}$

Plugging in values

$\rho=1.35*\frac{\pi*.0038^2}{.038}$

$1.61*10^{-3}\Omega*meters=\rho$

A resistor is made out of a material. The resistor has a cross-sectional area of and a length of . It is found to have a resistance of $6\Omega$ . Determine the resistivity of the material.

$4\Omega\cdot mm$

None of these

$6\Omega\cdot mm$

$4\Omega\cdot mm$

$2\Omega\cdot mm$

Explanation

Use the equation for resistivity:

$\rho=R\frac{A}{l}$

Plugging in values

$\rho=6*\frac{2}{3}$

$\rho=4\Omega\cdot mm$

A cylindrical resistor is long with a diameter of . Determine the resistivity of the material if the resistance is $50\Omega$ .

$.0209\Omega\cdot m$

$.567\Omega \cdot m$

$.805\Omega*m$

$.0714\Omega\cdot m$

$.0626\Omega\cdot m$

Explanation

Use the following relationship:

$\rho=R\frac{A}{l}$

Where $\rho$ is the resistivity

is the resistance

is the length

is the cross sectional area

Convert and to and plug in values:

$\rho=50*\frac{.002^2*\pi}{.03}$

$.0209\Omega\cdot m=\rho$

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 $935\Omega$ .

What is the resistivity of "Type F?"

$45.8\Omega\cdot meters$

None of these

$30.9 \Omega\cdot meters$

$12.1 \Omega\cdot meters$

$39.1 \Omega\cdot meters$

Explanation

We will use the relationship

$\rho=R\frac{A}{l}$

Where $\rho$ 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

$A=\pi\cdot r^2$

Combining our equations we get

$\rho=R\frac{\pi\cdot r^2}{l}$

We then need to plug in our values

$\rho=935\frac{\pi\cdot{.0265}^2}{.045}$

$45.8\Omega\cdot meters=\rho$

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 $.75\Omega$ . What is the resistivity of this material?

$1.88 *10^{-3} \Omega\cdot m$

None of these

$1.70 *10^{ -3} \Omega \cdot m$

$3.70 *10^{ -3} \Omega \cdot m$

$4.50 *10^{ -3} \Omega \cdot m$

Explanation

Use the relationship:

$\rho =R\frac{A}{l}$

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

The area of a circle is:

$A=\pi r^2$

Substitute:

$\rho =R\frac{\pi r^2}{l}$

Plug in given values and solve

$\rho =.75\Omega \frac{\pi (.006m)^2}{.045m}$

$\rho = 1.88 *10^{-3} \Omega\cdot m$

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?

$.0293 \Omega*meters$

None of these

$.0333 \Omega*meters$

$.0750 \Omega*meters$

$.0375 \Omega*meters$

Explanation

Using the relationship

$\rho=R\frac{A}{l}$

Where $\rho$ 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

$A=\pi*r^2$

Combining equations

$\rho=R\frac{\pi*r^2}{l}$

Plugging in values

$\rho=10.5\frac{\pi*.0065^2}{.0475}$

$.0293 \Omega*meters=\rho$

A resistor is made out of a material. The resistor has a cross-sectional area of and a length of . It is found to have a resistance of $7\Omega$ . A new resistor is built that has a length of and a cross sectional area of . Determine the resistance of the new resistor.

$6.36\Omega$

None of these

$7.77\Omega$

$3.95\Omega$

$4.05\Omega$

Explanation

Using

$\rho=R\frac{A}{l}$

Plugging in values

$\rho=7*\frac{4}{8}$

$\rho=3.5\Omega*mm$

Using

$R=\rho*\frac{l}{A}$

Plugging in values

$R=3.5*\frac{6}{3.3}$

$R=6.36\Omega$

A resistor is made out of a material. The resistor has a cross-sectional area of and a length of . It is found to have a resistance of $6\Omega$ . A new resistor is built that has a length of and a cross sectional area of . Determine the resistance of the new resistor.