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AP Physics 2 : Resistivity

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Example Question #21 : Resistivity

A resistor is made out of a material. The resistor has a cross-sectional area of 4mm^2 and a length of 8mm . It is found to have a resistance of $7\Omega$ . A new resistor is built that has a length of 6mm and a cross sectional area of 3.3mm^2 . Determine the resistance of the new resistor.

Possible Answers:

None of these

$6.36\Omega$

$3.95\Omega$

$4.05\Omega$

$7.77\Omega$

Correct answer:

$6.36\Omega$

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

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

$R=6.36\Omega$

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Example Question #22 : Resistivity

identical resistors are placed in parallel. They are placed in a circuit with a battery. If the current through the battery is , determine the resistivity of each resistor. Each resistor is 3cm long and has a diameter of 1cm .

Possible Answers:

$\rho_1=\rho_2=\rho_3=.79\Omega\cdot cm$

$\rho_1=\rho_2=\rho_3=2.27\Omega\cdot cm$

None of these

$\rho_1=\rho_2=\rho_3=1.50\Omega\cdot cm$

$\rho_1=.79\Omega\cdot cm$

$\rho_2=\rho_3=1.50\Omega\cdot cm$

Correct answer:

$\rho_1=\rho_2=\rho_3=.79\Omega\cdot cm$

Explanation:

Since each resistor is in parallel, the voltage drop across each will be .

Since each resistor is identical, they all have the same resistance.

Using

$I_1+I_2+I_3=I_{total}=3A$

and

I_1=I_2=I_3

It is determined that

I_1=I_2=I_3=1A

Using

V=IR

3=1*R

$R=3\Omega$ for all three resistors

Using definition of resistivity:

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

$\rho=3*\frac{\pi*.5^2}{3}$

$\rho=.79\Omega\cdot cm$

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Example Question #23 : Resistivity

A resistor is made out of a material. The resistor has a cross-sectional area of 2mm^2 and a length of 3mm . It is found to have a resistance of $6\Omega$ . Determine the resistivity of the material.

Possible Answers:

None of these

$6\Omega\cdot mm$

$2\Omega\cdot mm$

$4\Omega\cdot mm$

Correct answer:

$4\Omega\cdot mm$

Explanation:

Use the equation for resistivity:

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

Plugging in values

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

$\rho=4\Omega\cdot mm$

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Example Question #24 : Resistivity

A resistor is made out of a material. The resistor has a cross-sectional area of 2mm^2 and a length of 3mm . It is found to have a resistance of $6\Omega$ . A new resistor is built that has a length of 4mm and a cross sectional area of 1.5mm^2 . Determine the resistance of the new resistor.

Possible Answers:

$10.7\Omega$

None of these

$6.37\Omega$

$4.17\Omega$

$4\Omega$

Correct answer:

$10.7\Omega$

Explanation:

Use the equation for resistivity:

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

Plugging in values

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

$\rho=4\Omega\cdot mm$

Using

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

Plugging in values

$R=4*\frac{4}{1.5}$

$R=10.7\Omega$

Report an Error

Example Question #25 : Resistivity

Possible Answers:

.23A

None of these

.89A

.11A

.56A

Correct answer:

.56A

Explanation:

Use the equation for resistivity:

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

Plugging in values

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

$\rho=4\Omega\cdot mm$

Rearrange the same equation and solve for resistance:

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

Plugging in values

$R=4*\frac{4}{1.5}$

$R=10.7\Omega$

Use Ohm's law to find current:

V=IR

6=I*10.7

I=.56A

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Example Question #26 : Resistivity

A scientist is testing resistors made of the same material. Resistor has a cross sectional area of 3mm^2 and a length of 3mm^2 . Resistor has a cross sectional area of 6mm^2 and a length of 3mm^2 . How will the resistance of compare to that of ?

Possible Answers:

The resistance will quadruple

The resistance will stay the same

The resistance will be cut in half

None of these

The resistance will double

Correct answer:

The resistance will be cut in half

Explanation:

Use the equation for resistivity to visualize the proportions:

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

$\rho$ will stay constant as the material is the same. doubles and stays the same. Thus, the resistance, , will get cut in half.

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Example Question #21 : Resistivity

A resistor is made out of a material. The resistor has a cross-sectional area of 4mm^2 and a length of 8mm . It is found to have a resistance of $7\Omega$ . Determine the resistivity of the material.

Possible Answers:

$6.5\Omega\cdot mm$

$3.5\Omega\cdot mm$

$7.0\Omega\cdot mm$

$10.3\Omega\cdot mm$

$4.7\Omega\cdot mm$

Correct answer:

$3.5\Omega\cdot mm$

Explanation:

Using

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

Plugging in values

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

$\rho=3.5\Omega\cdot mm$

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Example Question #28 : Resistivity

Possible Answers:

None of these

.94A

3.25A

1.94A

1.25A

Correct answer:

.94A

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

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

$R=6.36\Omega$

Using

V=IR

Solving for

$I=\frac{V}{R}$

$I=\frac{6}{6.36}$

I=.94A

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Example Question #29 : Resistivity

A scientist is testing resistors made of the same material. Resistor has a cross sectional area of 4mm^2 and a length of 8mm . Resistor has a cross sectional area of 6mm^2 and a length of 3mm . How will the resistance of compare to that of ?

Possible Answers:

It is impossible to determine

The resistance of will be a quarter of that of

None of these

They will be the same

The resistance of will be a quarter of that of

Correct answer:

The resistance of will be a quarter of that of

Explanation:

Using

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

$\rho$ will stay constant as the material is the same. increases by a ratio of $\frac{3}{2}$ , and decreases by a ratio of $\frac{3}{8}$ . Thus, the resistance, , will decrease to a quarter of it's original value. $\left (\frac{\frac{3}{8}}{\frac{3}{2}}\right)$

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Example Question #30 : Resistivity

A cubic resistor is placed in a circuit. If each edge measures 1cm long, the voltage of the battery is and the current through the resistor is , determine the resistivity.

Possible Answers:

$1.67\Omega\cdot cm$

None of these

$6\Omega\cdot m$

$6\Omega\cdot cm$

$18\Omega\cdot cm$

Correct answer:

$6\Omega\cdot cm$

Explanation:

Determining the resistance

V=IR

6=1*R

$R=6\Omega$

Using

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

$\rho=6*\frac{1}{1}$

$\rho=6\Omega\cdot cm$

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AP Physics 2 : Resistivity

Study concepts, example questions & explanations for AP Physics 2

All AP Physics 2 Resources

Example Questions

Example Question #21 : Resistivity

Example Question #22 : Resistivity

Example Question #23 : Resistivity

Example Question #24 : Resistivity

Example Question #25 : Resistivity

Example Question #26 : Resistivity

Example Question #21 : Resistivity

Example Question #28 : Resistivity

Example Question #29 : Resistivity

Example Question #30 : Resistivity

All AP Physics 2 Resources

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