AP Physics C Electricity and Magnetism Quiz: Resistance Resistivity And Ohms Law

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Resistance Resistivity And Ohms LawQuestion 1 of 20

Wire A has length $L$ and radius $r$ . Wire B, made from the same uniform material, has length $2L$ and radius $r/2$ . What is the ratio of the resistance of Wire B to the resistance of Wire A, $R_B/R_A$ ?

1

2

4

8

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AP Physics C Electricity and Magnetism Quiz

AP Physics C Electricity and Magnetism Quiz: Resistance Resistivity And Ohms Law

Practice Resistance Resistivity And Ohms Law in AP Physics C Electricity and Magnetism with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Resistance Resistivity And Ohms Law, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Physics C Electricity and Magnetism.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

$1$
$2$
$4$
$8$ (correct answer)

Explanation: Resistance is given by

R = \rho L/A

, where

A = \pi r^2

. For Wire A,

R_A = \rho L/(\pi r^2)

. For Wire B,

L_B=2L

and

r_B=r/2

, so

A_B = \pi(r/2)^2 = \pi r^2/4

. Thus,

R_B = \rho(2L)/(\pi r^2/4) = 8(\rho L/(\pi r^2)) = 8R_A

. The ratio

R_B/R_A

is 8.

Question 2

The potential difference $V$ across a circuit component is measured as a function of the current $I$ through it. A plot of $V$ as a function of $I$ results in a straight line passing through the origin with a slope of $200\,\text{V/A}$ . What is the resistance of the component?

$0.005\,\Omega$
$100\,\Omega$
$200\,\Omega$ (correct answer)
$400\,\Omega$

Explanation: From Ohm's Law,

V=IR

. A graph of

V

(y-axis) versus

I

(x-axis) for an ohmic resistor is a straight line with slope

m = \Delta V / \Delta I

. This slope is equal to the resistance

R

. Therefore, the resistance of the component is

200\,\Omega

Question 3

A material is classified as non-ohmic. What does this classification imply about the material's resistance?

The resistance is zero under all conditions, meaning it is a perfect superconductor.
The resistance is constant regardless of the applied voltage or resulting current.
The resistance varies as the potential difference across it or the current through it changes. (correct answer)
The resistance is infinite under all conditions, meaning it is a perfect insulator.

Explanation: A non-ohmic material is one that does not follow Ohm's Law, which states that the ratio of voltage to current (the resistance) is constant. Therefore, for a non-ohmic material, the resistance changes depending on the operating conditions like voltage or current.

Question 4

A student collects the following data for the potential difference across and current through an unknown circuit element.

Potential Difference (V): 2.0, 4.0, 6.0, 8.0 Current (A): 0.50, 1.00, 1.50, 2.00

Based on the provided data, which of the following conclusions is most justified?

The element is ohmic with a resistance of $4.0\,\Omega$ . (correct answer)
The element is ohmic with a resistance of $0.25\,\Omega$ .
The element is non-ohmic because the current increases as the voltage increases.
The element is non-ohmic because the relationship is not specified to be at constant temperature.

Explanation: To determine if the element is ohmic, we calculate the ratio

R = V/I

for each data point:

2.0/0.50 = 4.0\,\Omega

4.0/1.00 = 4.0\,\Omega

6.0/1.50 = 4.0\,\Omega

, and

8.0/2.00 = 4.0\,\Omega

. Since the ratio is constant, the element is ohmic with a resistance of

4.0\,\Omega

Question 5

A metallic resistor is used in a circuit that operates in a thermally controlled environment. If the operating temperature is significantly increased, what is the expected effect on the resistor's resistance?

The resistance will increase due to the positive temperature coefficient of resistivity for metals. (correct answer)
The resistance will decrease as the thermal expansion increases the conductor's volume.
The resistance will remain unchanged, as it depends only on the material's geometry.
The resistance will become zero if the temperature exceeds a critical threshold value.

Explanation: For most metallic conductors, resistivity increases with temperature. This is described by a positive temperature coefficient of resistivity. Since resistance

R

is directly proportional to resistivity

\rho

(

R = \rho L/A

), an increase in temperature will cause an increase in the resistance of the metallic resistor.

Question 6

A rod of length $L$ and uniform cross-sectional area $A$ is made of a material whose resistivity varies along its length according to the function $\rho(x) = \rho_0(1 + x^2/L^2)$ , where $x$ is the distance from one end. What is the total resistance of the rod?

$\frac{\rho_0 L}{A}$
$\frac{2\rho_0 L}{A}$
$\frac{4\rho_0 L}{3A}$ (correct answer)
$\frac{3\rho_0 L}{2A}$

Explanation: The resistance

dR

of an infinitesimal slice of length

dx

dR = \rho(x) \frac{dx}{A}

. To find the total resistance, we integrate from

x=0

x=L

R = \int_0^L \frac{\rho_0}{A}(1 + \frac{x^2}{L^2}) dx = \frac{\rho_0}{A} \left[x + \frac{x^3}{3L^2}\right]_0^L = \frac{\rho_0}{A} \left(L + \frac{L^3}{3L^2}\right) = \frac{\rho_0}{A} \left(L + \frac{L}{3}\right) = \frac{4\rho_0 L}{3A}

Question 7

A potential difference of $1.0\,\text{V}$ is applied across a cylindrical wire of length $2.0\,\text{m}$ and radius $0.50\,\text{mm}$ . A current of $4.0\,\text{A}$ is measured. What is the resistivity of the wire's material?

$9.8 \times 10^{-8}\,\Omega \cdot \text{m}$ (correct answer)
$1.6 \times 10^{-7}\,\Omega \cdot \text{m}$
$3.1 \times 10^{-6}\,\Omega \cdot \text{m}$
$6.3 \times 10^{-6}\,\Omega \cdot \text{m}$

Explanation: First, calculate the resistance using Ohm's Law:

R = V/I = 1.0\,\text{V} / 4.0\,\text{A} = 0.25\,\Omega

. Next, calculate the cross-sectional area:

A = \pi r^2 = \pi (0.50 \times 10^{-3}\,\text{m})^2 \approx 7.85 \times 10^{-7}\,\text{m}^2

. Finally, use the resistance formula to find resistivity:

\rho = RA/L = (0.25\,\Omega)(7.85 \times 10^{-7}\,\text{m}^2) / (2.0\,\text{m}) \approx 9.8 \times 10^{-8}\,\Omega \cdot \text{m}

Question 8

Considering the information provided, a lightbulb in a household circuit obeys $V=IR$ ; resistance $R$ (Ω) controls current, and resistivity $\rho$ (in $\Omega\cdot\text{m}$ ) is intrinsic to the filament material. What happens to current if resistance increases and voltage remains constant according to Ohm's Law ( $V=IR$ )?

Current increases as resistance increases
Current decreases as resistance increases (correct answer)
Voltage becomes measured in amperes (A)
Resistance decreases as resistivity increases

Explanation: This question tests understanding of resistance, resistivity, and Ohm's Law in AP Physics C: Electricity and Magnetism. Ohm's Law V = IR shows that for constant voltage, current and resistance have an inverse relationship, expressed as I = V/R. In the lightbulb circuit example, when the filament's resistance increases while the applied voltage remains constant, the current through the bulb must decrease to satisfy Ohm's Law. Choice B is correct because it accurately states that current decreases as resistance increases when voltage is constant, following directly from the mathematical relationship I = V/R. Choice A is incorrect as it suggests a direct relationship between current and resistance, which would violate Ohm's Law and conservation principles. Students should understand that increased resistance means more opposition to current flow, like a dimmer switch increasing resistance to reduce bulb brightness. Practice with real circuits helps: a 60W bulb has lower resistance than a 40W bulb, so it draws more current at the same voltage.

Question 9

Considering the information provided, a lightbulb in a household circuit follows Ohm's Law $V=IR$ , where $R$ (in $\Omega$ ) limits $I$ (in A). Resistivity $\rho$ (in $\Omega\cdot\text{m}$ ) is a material property affecting $R$ . What happens to current if resistance increases and voltage remains constant according to $V=IR$ ?

Current increases because $R$ opposes voltage
Current decreases because $I = V/R$ (correct answer)
Current remains the same because $V$ is fixed
Current becomes equal to $R$ because $V=IR$

Explanation: This question tests understanding of resistance, resistivity, and Ohm's Law in AP Physics C: Electricity and Magnetism. Ohm's Law V = IR rearranges to I = V/R, establishing that current is inversely proportional to resistance when voltage remains constant in a circuit. In the lightbulb example, if the filament's resistance increases while the household circuit maintains constant voltage, the current through the bulb must decrease according to the relationship I = V/R. Choice B is correct because it states that current decreases and provides the correct mathematical relationship I = V/R that governs this inverse proportionality. Choice D is incorrect because it misinterprets Ohm's Law - current does not become equal to resistance; rather, current equals voltage divided by resistance, and they have different units (amperes vs ohms). Students should practice dimensional analysis with Ohm's Law to verify relationships and avoid unit confusion. Emphasize that in household circuits, voltage is typically fixed by the power company, making resistance the primary variable for controlling current in devices.

Question 10

Two wires of identical length and diameter are connected to identical batteries. Wire 1 is made of copper ( $\rho_C \approx 1.7 \times 10^{-8}\,\Omega \cdot \text{m}$ ) and Wire 2 is made of nichrome ( $\rho_N \approx 1.1 \times 10^{-6}\,\Omega \cdot \text{m}$ ). How does the current $I_C$ in the copper wire compare to the current $I_N$ in the nichrome wire?

$I_C$ is much greater than $I_N$ . (correct answer)
$I_C$ is much less than $I_N$ .
$I_C$ is approximately equal to $I_N$ .
The relationship cannot be determined without knowing the battery voltage.

Explanation: Since the wires have identical dimensions, their resistances are directly proportional to their resistivities (

R = \rho L/A

). Copper has a much lower resistivity than nichrome, so the copper wire has a much lower resistance. With identical batteries (same voltage

V

), the current (

I=V/R

) will be much larger in the wire with lower resistance, so

I_C

is much greater than

I_N

Question 11

Considering the information provided, a household device follows $V=IR$ ; resistance $R$ (Ω) is the circuit-level opposition to current, while resistivity $\rho$ (in $\Omega\cdot\text{m}$ ) is intrinsic to the material. What happens to current if resistance increases and voltage remains constant according to Ohm's Law ( $V=IR$ )?

Current increases because $I=VR$
Current decreases because $I=V/R$ (correct answer)
Voltage decreases because $V=I/R$
Current stays constant regardless of $R$

Explanation: This question tests understanding of resistance, resistivity, and Ohm's Law in AP Physics C: Electricity and Magnetism. Ohm's Law V = IR can be rearranged to I = V/R, clearly showing that current equals voltage divided by resistance. In the household device example, when resistance increases while voltage stays constant, the current must decrease according to this inverse relationship shown in the equation I = V/R. Choice B is correct because it both states the correct outcome (current decreases) and provides the correct mathematical relationship (I = V/R) that explains why this happens. Choice A is incorrect because it presents a mathematically impossible equation I = VR, which would have incorrect units and suggest current increases with resistance. Students should always check their equation rearrangements using dimensional analysis: I[A] = V[V]/R[Ω] gives correct units, while I = VR would give units of V·Ω, not amperes. Understanding the mathematical form reinforces the conceptual inverse relationship.

Question 12

A resistor is shaped like a truncated cone of length $L$ and has uniform resistivity $\rho$ . The radius varies linearly with position $x$ from $r_1$ at $x=0$ to $r_2$ at $x=L$ . The current is directed along the x-axis. Which of the following expressions represents the resistance of a thin disk of the material with thickness $dx$ at position $x$ ?

$\rho \frac{dx}{\pi [r(x)]^2}$ (correct answer)
$\rho \frac{2\pi r(x) dx}{L}$
$\frac{dx}{\rho \pi [r(x)]^2}$
$\rho \frac{dx}{2\pi r(x)L}$

Explanation: The resistance of a small element is given by

dR = \rho \frac{d(\text{length})}{A}

. For a thin disk of thickness

dx

oriented perpendicular to the current flow, the length is

dx

and the cross-sectional area is

A(x) = \pi [r(x)]^2

. Therefore, the resistance of the thin disk is

dR = \rho \frac{dx}{\pi [r(x)]^2}

Question 13

A cylindrical conductor has length $L$ , radius $r$ , and resistance $R$ . A second conductor made of the same material has length $L/2$ and radius $2r$ . What is the resistance of the second conductor?

$R/8$ (correct answer)
$R/4$
$R$
$2R$

Explanation: The resistance

R

is given by

R = \rho L/A = \rho L/(\pi r^2)

. The new resistance

R_{\text{new}}

is for a wire with length

L_{\text{new}} = L/2

and radius

r_{\text{new}} = 2r

. So,

R_{\text{new}} = \rho (L/2) / (\pi (2r)^2) = \rho (L/2) / (4\pi r^2) = (1/8) (\rho L / (\pi r^2)) = R/8

Question 14

A potential difference $V$ is applied across an ohmic resistor, resulting in a current $I$ . If the potential difference is doubled to $2V$ while the temperature of the resistor remains constant, what is the new current?

$I/2$
$I$
$2I$ (correct answer)
$4I$

Explanation: For an ohmic resistor, the resistance

R

is constant. According to Ohm's Law,

I = V/R

. The new current is

I_{\text{new}} = V_{\text{new}}/R = (2V)/R = 2(V/R) = 2I

. The current is directly proportional to the potential difference.

Question 15

Two cylindrical wires, X and Y, are made of different materials and have different dimensions. The resistance of Wire X is greater than the resistance of Wire Y. Which of the following statements provides a sufficient condition for the resistivity of material X to be greater than that of material Y?

The length of wire X is greater than the length of wire Y.
The cross-sectional area of wire X is smaller than the cross-sectional area of wire Y.
The ratio of length to area ( $L/A$ ) for wire X is less than or equal to that of wire Y. (correct answer)
The current through wire X is less than the current through wire Y for the same applied voltage.

Explanation: We are given

R_X > R_Y

, which means

(\rho_X L_X / A_X) > (\rho_Y L_Y / A_Y)

. We want to find a condition that guarantees

\rho_X > \rho_Y

. If we know that

(L_X / A_X) \le (L_Y / A_Y)

, then for the inequality

R_X > R_Y

to hold, it must be true that

\rho_X > \rho_Y

. The other options do not provide sufficient information.

Question 16

The current $I$ through a circuit component is measured as a function of the potential difference $V$ across it. A plot of $I$ as a function of $V$ is a straight line passing through the origin with a slope of $0.05\,\text{A/V}$ . What is the resistance of the component?

$0.05\,\Omega$
$10\,\Omega$
$20\,\Omega$ (correct answer)
$25\,\Omega$

Explanation: The graph shows

I

(y-axis) versus

V

(x-axis). For an ohmic resistor, the slope of this graph is

m = \Delta I / \Delta V

. According to Ohm's Law,

R = V/I

, so the resistance is the reciprocal of the slope:

R = 1/m = 1/(0.05\,\text{A/V}) = 20\,\Omega

Question 17

The filament of an incandescent light bulb is made of tungsten. As current passes through it, its temperature increases significantly. How does this temperature increase affect the filament's resistance, and why?

The resistance increases because the increased thermal vibrations of the tungsten atoms impede the flow of electrons. (correct answer)
The resistance decreases because the higher thermal energy provides more free electrons for conduction.
The resistance remains constant because resistivity is an intrinsic property independent of temperature.
The resistance decreases because the filament expands, increasing its cross-sectional area for current flow.

Explanation: Tungsten is a metallic conductor. For such materials, resistivity increases with temperature. The increased temperature causes the metal's lattice ions to vibrate with greater amplitude, which increases the frequency of collisions with conduction electrons, thus impeding their flow and increasing resistance.

Question 18

A uniform potential difference is applied across the ends of a cylindrical ohmic conductor. If the potential difference is tripled, what is the effect on the average drift velocity of the charge carriers within the conductor, assuming its properties remain unchanged?

It decreases to one-third its original value.
It remains the same.
It increases by a factor of three. (correct answer)
It increases by a factor of nine.

Explanation: Tripling the potential difference

V

across an ohmic conductor triples the current

I

(

I=V/R

). The current is related to drift velocity

v_d

I = nqAv_d

, where

n, q,

and

A

are constants for the wire. Therefore, if

I

is tripled,

v_d

must also be tripled.

Question 19

A potential difference is applied to a resistor made of a material that obeys Ohm's law. If the resistor is replaced by another one made of the same material but with twice the length and twice the diameter, how does the new current compare to the original current for the same applied potential difference?

The current is halved.
The current is unchanged.
The current is doubled. (correct answer)
The current is quadrupled.

Explanation: The original resistance is

R_1 = \rho L/A_1

, where

A_1 = \pi (d/2)^2

. The new resistor has length

2L

and diameter

2d

, so its area is

A_2 = \pi (2d/2)^2 = 4 \pi(d/2)^2 = 4A_1

. The new resistance is

R_2 = \rho(2L)/(4A_1) = (1/2)(\rho L/A_1) = R_1/2

. Since the potential difference is the same, the new current

I_2 = V/R_2 = V/(R_1/2) = 2(V/R_1) = 2I_1

. The current is doubled.

Question 20

A potential difference of $12\,\text{V}$ is maintained across an ohmic resistor with a resistance of $150\,\Omega$ . What is the current flowing through the resistor?

$0.080\,\text{A}$ (correct answer)
$12.5\,\text{A}$
$1800\,\text{A}$
$0.0083\,\text{A}$

Explanation: According to Ohm's Law, the current

I

is given by

I = V/R

. Substituting the given values:

I = 12\,\text{V} / 150\,\Omega = 0.080\,\text{A}