AP Physics 2: Algebra-Based Practice Quiz: Resistance, Resistivity, and Ohm's Law

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

Which of the following best describes electrical resistance?

A)A measure of how strongly a material opposes the movement of electric charge.B)A fundamental property of a material based on its atomic structure.C)The flow of electric charge per unit of time.D)The potential difference across an element in a circuit.

All Questions (16)

Which of the following best describes electrical resistance?

A) A measure of how strongly a material opposes the movement of electric charge.

B) A fundamental property of a material based on its atomic structure.

C) The flow of electric charge per unit of time.

D) The potential difference across an element in a circuit.

Correct Answer: A

Based on the provided content, 'Resistance is a measure of the degree to which an object opposes the movement of electric charge.' Option B describes resistivity, not resistance. Options C and D describe current and potential difference, respectively.

A cylindrical copper wire has a length L and a cross-sectional area A. If the wire is replaced by another copper wire with length 2L but the same cross-sectional area A, how does the resistance of the new wire compare to the original?

A) The new resistance is half the original resistance.

B) The new resistance is the same as the original resistance.

C) The new resistance is double the original resistance.

D) The new resistance is four times the original resistance.

Correct Answer: C

The resistance of a wire is given by the equation R = ρl/A. Since resistance (R) is directly proportional to the length (l), doubling the length while keeping the resistivity (ρ) and cross-sectional area (A) constant will double the resistance.

According to Ohm's law, if the potential difference across an ohmic resistor is doubled, what happens to the current flowing through it?

A) The current is halved.

B) The current remains the same.

C) The current is doubled.

D) The current is quadrupled.

Correct Answer: C

Ohm's law is stated as I = ΔV/R. For an ohmic material, the resistance R is constant. Therefore, the current (I) is directly proportional to the potential difference (ΔV). If the potential difference is doubled, the current must also double.

Which term describes a fundamental property of a material that quantifies how strongly it opposes the motion of electric charge, based on its atomic and molecular structure?

A) Resistance

B) Current

C) Potential Difference

D) Resistivity

Correct Answer: D

The provided content defines resistivity as 'a fundamental property of a material that depends on its atomic and molecular structure and quantifies how strongly the material opposes the motion of electric charge.' Resistance, in contrast, depends on the object's geometry (length and area) as well as the material.

A wire of length L and cross-sectional area A has a resistance R. A second wire made of the same material has a length of L/2 and a cross-sectional area of 2A. What is the resistance of the second wire?

A) 4R

B) R

C) R/2

D) R/4

Correct Answer: D

Resistance is calculated using R = ρl/A. For the second wire, the new length l' = L/2 and the new area A' = 2A. The new resistance R' = ρ(l')/(A') = ρ(L/2)/(2A) = ρL/(4A) = (1/4) * (ρL/A). Since the original resistance R = ρL/A, the new resistance is R/4.

Two wires, X and Y, are made of the same ohmic material. Wire X is twice as long as wire Y, but has half the cross-sectional area of wire Y. If the same potential difference is applied across both wires, how does the current in wire X (I_X) compare to the current in wire Y (I_Y)?

A) I_X = 4 * I_Y

B) I_X = 2 * I_Y

C) I_X = I_Y / 2

D) I_X = I_Y / 4

Correct Answer: D

First, find the ratio of resistances. R = ρl/A. R_X = ρ(2l_Y)/(A_Y/2) = 4 * (ρl_Y/A_Y) = 4R_Y. According to Ohm's Law, I = ΔV/R. Since ΔV is the same for both, I_X = ΔV/R_X = ΔV/(4R_Y) = (1/4) * (ΔV/R_Y) = I_Y / 4.

What is the defining characteristic of a material that obeys Ohm's law?

A) It has zero resistance.

B) Its resistance is constant for all currents.

C) Its resistance increases with temperature.

D) It is a perfect insulator.

Correct Answer: B

The provided text states, 'Materials that obey Ohm's law have constant resistance for all currents and are called ohmic materials.' This is the definition of an ohmic material.

An engineer has a sample of aluminum and a sample of copper of identical size and shape. Which of the following quantities will be different for the two samples?

A) Length

B) Cross-sectional area

C) Resistivity

D) Volume

Correct Answer: C

Resistivity is a fundamental property of a material that depends on its atomic and molecular structure. Since aluminum and copper are different materials, they will have different resistivities. Length, area, and volume are geometric properties, which are stated to be identical for the two samples.

A potential difference of 12 V is applied across a resistor with a resistance of 4 Ω. What is the current flowing through the resistor?

A) 0.33 A

B) 3 A

C) 16 A

D) 48 A

Correct Answer: B

Using Ohm's law, I = ΔV/R. Given ΔV = 12 V and R = 4 Ω, the current I = 12 V / 4 Ω = 3 A.

A wire has a resistance R. A second wire, made of the same material, is constructed to have double the length and half the cross-sectional area. What is the resistance of the second wire?

A) R/4

B) R

C) 2R

D) 4R

Correct Answer: D

Resistance is given by R = ρl/A. The new wire has length l' = 2l and area A' = A/2. The new resistance R' = ρ(l')/(A') = ρ(2l)/(A/2) = 4 * (ρl/A). Since the original resistance was R = ρl/A, the new resistance is 4R.

To create a conductor with the lowest possible resistance using a given material, what geometric properties should it have?

A) Short length and large cross-sectional area.

B) Short length and small cross-sectional area.

C) Long length and large cross-sectional area.

D) Long length and small cross-sectional area.

Correct Answer: A

The formula for resistance is R = ρl/A. To minimize R, one must minimize the numerator and maximize the denominator. Therefore, the length (l) should be as short as possible, and the cross-sectional area (A) should be as large as possible.

A uniform wire has a length of 2.0 m and a cross-sectional area of 4.0 x 10^-6 m^2. If the material's resistivity is 1.0 x 10^-6 Ω·m, what is the resistance of the wire?

A) 0.5 Ω

B) 2.0 Ω

C) 8.0 Ω

D) 0.125 Ω

Correct Answer: A

Using the formula R = ρl/A: R = (1.0 x 10^-6 Ω·m) * (2.0 m) / (4.0 x 10^-6 m^2). R = (2.0 x 10^-6) / (4.0 x 10^-6) Ω = 0.5 Ω.

A constant potential difference is maintained across an ohmic resistor. If the resistance of the circuit element is doubled, how is the current affected?

A) The current is quadrupled.

B) The current is doubled.

C) The current is halved.

D) The current remains unchanged.

Correct Answer: C

Ohm's law states I = ΔV/R. Since the potential difference ΔV is constant, the current I is inversely proportional to the resistance R. If the resistance is doubled, the current will be halved.

An ohmic conducting wire is stretched to twice its original length. Assuming the volume and resistivity of the material remain constant, by what factor does its resistance change?

A) It is halved.

B) It stays the same.

C) It is doubled.

D) It is quadrupled.

Correct Answer: D

The volume of the wire is V = A * l. If the volume is constant, A * l = A' * l'. Since the new length l' = 2l, the new area must be A' = A * l / l' = A * l / (2l) = A/2. Now, use the resistance formula R = ρl/A. The new resistance is R' = ρ(l')/(A') = ρ(2l)/(A/2) = 4 * (ρl/A) = 4R. The resistance is quadrupled.

Wire X has length L and radius r. Wire Y is made of a material with twice the resistivity of wire X. If wire Y is to have the same resistance as wire X, and has a length of 2L, what must be its radius?

A) r / 2

B) r

C) 2r

D) 4r

Correct Answer: C

Resistance is R = ρl/A = ρl/(πr^2). We are given R_X = R_Y. So, ρ_X * L / (π * r_X^2) = ρ_Y * L_Y / (π * r_Y^2). We know ρ_Y = 2ρ_X, L_Y = 2L, and r_X = r. Substituting these in: ρ_X * L / (πr^2) = (2ρ_X) * (2L) / (π * r_Y^2). The terms ρ_X, L, and π cancel out. 1/r^2 = 4/r_Y^2. Rearranging gives r_Y^2 = 4r^2, so r_Y = 2r.

For an ohmic device, a graph of potential difference (ΔV) as a function of current (I) is created. What does the slope of this graph represent?

A) Resistivity

B) Resistance

C) The inverse of resistance (conductance)

D) The inverse of resistivity

Correct Answer: B

Ohm's law can be written as ΔV = I * R. This is in the form of a linear equation y = mx + b, where y = ΔV, x = I, and the y-intercept b = 0. The slope (m) is therefore the resistance (R). A graph of ΔV (on the y-axis) vs. I (on the x-axis) will be a straight line through the origin with a slope equal to the resistance.