AP Physics 2: Algebra-Based Unit 3: Electric Circuits Practice Exam

Assessment for Unit 3: Electric Circuits

Estimated Time: 60 minutes

Exam Details

Questions: 28 total (28 multiple choice)
Time: 60 minutes (recommended)
Topics Covered: Unit 3: Electric Circuits
Format: Multiple Choice questions matching real exam difficulty
Scoring: Instant results with detailed explanations

A. Multiple-Choice Questions (28 Questions)

Select the one best answer for each question.

1. [Skill: 5.1 | Topic: 3.5] A non-ideal battery with electromotive force (emf) $\epsilon$ and internal resistance $r$ is connected to a variable external resistor $R_{load}$. An ideal voltmeter is connected across the terminals of the battery. If the resistance of $R_{load}$ is increased, which of the following describes the resulting changes in the current $I$ through the circuit and the terminal voltage $V_t$ measured by the voltmeter?

(A)The current $I$ increases and the terminal voltage $V_t$ increases.(B)The current $I$ increases and the terminal voltage $V_t$ decreases.(C)The current $I$ decreases and the terminal voltage $V_t$ increases.(D)The current $I$ decreases and the terminal voltage $V_t$ decreases.

2. [Skill: 4.2 | Topic: 3.5] A student is tasked with measuring the resistance of a specific resistor $R_x$ within a multi-loop compound DC circuit. To do this, the student must measure the current through $R_x$ and the potential difference across $R_x$ simultaneously. Which of the following describes the correct connection for the measuring instruments?

(A)An ideal ammeter should be connected in parallel with $R_x$, and an ideal voltmeter should be connected in series with $R_x$.(B)An ideal ammeter should be connected in series with $R_x$, and an ideal voltmeter should be connected in parallel with $R_x$.(C)Both the ideal ammeter and the ideal voltmeter should be connected in series with $R_x$.(D)Both the ideal ammeter and the ideal voltmeter should be connected in parallel with $R_x$.

3. [Skill: 6.4 | Topic: 3.6] A student is analyzing a complex circuit containing multiple batteries and resistors. The student uses Kirchhoff's loop rule to write an equation for one of the closed paths in the circuit. Which of the following fundamental physical principles provides the theoretical justification for the use of Kirchhoff's loop rule?

(A)The conservation of electric charge, because the total current entering a junction must equal the total current leaving it.(B)The conservation of energy, because the work done by the electric field on a charge moving around a closed path must be zero.(C)Newton's third law, because the force exerted by the battery on the charges is equal and opposite to the force exerted by the resistors.(D)The conservation of linear momentum, because the drift velocity of the electrons remains constant throughout the steady-state circuit.

4. **3.** [Skill: 6.4 | Topic: 3.7] Kirchhoff’s junction rule states that the total current entering a junction must equal the total current leaving the junction. Which fundamental physical principle is the basis for this rule? (A) Conservation of Energy (B) Conservation of Linear Momentum (C) Conservation of Electric Charge (D) Newton's Third Law of Motion

(A)Conservation of Energy(B)Conservation of Linear Momentum(C)Conservation of Electric Charge(D)Newton's Third Law of Motion

5. [Skill: 2.2 | Topic: 3.8] A student is given three capacitors with capacitances $C_1 = 6.0\, \mu F$, $C_2 = 3.0\, \mu F$, and $C_3 = 4.0\, \mu F$. The student connects $C_1$ and $C_2$ in series with each other, and then connects this series combination in parallel with $C_3$. What is the equivalent capacitance of the entire network?

(A)1.3 $\mu $F(B)2.0 $\mu $F(C)6.0 $\mu $F(D)13.0 $\mu $F

Refer to the figure below.

6. [Skill: 2.2 | Topic: 3.1] A student uses a sensor to measure the total net charge $q$ that has passed through a cross-section of a copper wire as a function of time $t$. The data is plotted on the graph described below. Based on the graph, what is the magnitude of the steady electric current flowing through the wire? [Image Cue]: Line graph, Charge vs. Time, Vertical axis: Charge $q$ (C) from 0 to 10, Horizontal axis: Time $t$ (s) from 0 to 5. The graph shows a linear relationship passing through the origin $(0,0)$ and the point $(4.0, 8.0)$.

(A)0.5 A(B)2.0 A(C)4.0 A(D)32 A

7. [Skill: 6.4 | Topic: 3.1] Two identical neutral metal spheres, Sphere 1 and Sphere 2, are connected by a thin copper wire. A third positively charged rod is brought near Sphere 1 but does not touch it. While the rod is held in place, a student observes a momentary current in the wire. Which of the following best explains why a sustained current is NOT produced in this arrangement?

(A)The copper wire is a conductor, which prevents the buildup of a potential difference.(B)The charges in the spheres reach a new electrostatic equilibrium, eliminating the electric potential difference across the wire.(C)The rod only exerts a force on the protons in the wire, and protons are too massive to maintain a current.(D)Electric current can only be sustained if the total net charge of the two-sphere system is non-zero.

8. [Skill: 1.4 | Topic: 3.1] In a specific vacuum tube, a beam of electrons moves horizontally from left to right. Which of the following correctly describes the direction of the conventional current and the reason for that direction?

(A)The conventional current is directed from left to right because it follows the direction of the physical motion of the charge carriers.(B)The conventional current is directed from left to right because the potential is higher on the left side of the tube.(C)The conventional current is directed from right to left because it is defined as the direction that positive charge would move.(D)The conventional current is directed from right to left because electrons always move from regions of high potential to regions of low potential.

9. [Skill: 1.1 | Topic: 3.2] A student is tasked with constructing a circuit based on a specific requirement: a single 12V battery must power two identical lamps, $L_1$ and $L_2$. The circuit must be designed such that $L_1$ is always on when the battery is connected, but $L_2$ can be toggled on or off using a switch without affecting the operation of $L_1$. Which of the following physical arrangements, when represented as a schematic, meets these criteria?

(A)A series circuit where the battery, the switch, $L_1$, and $L_2$ are all connected in a single continuous loop.(B)A circuit where the battery is in series with $L_1$, and this combination is then placed in parallel with a branch containing only the switch and $L_2$.(C)A circuit where the battery is connected to two parallel branches; the first branch contains only $L_1$, and the second branch contains the switch and $L_2$ connected in series.(D)A circuit where the battery is in series with the switch, and the switch is in series with a parallel combination of $L_1$ and $L_2$.

Refer to the figure below.

10. [Skill: 1.2 | Topic: 3.2] A circuit is constructed according to the schematic described below. Which of the following conditions will result in ONLY lightbulbs $L_1$ and $L_3$ being lit? [Image Cue]: Circuit Schematic. A battery is connected to a main wire. Switch $S_1$ is located on this main wire. The wire then reaches a junction that splits into two parallel branches. Branch A contains lightbulb $L_2$ and switch $S_2$ connected in series. Branch B contains lightbulb $L_3$. The two branches then rejoin into a single wire that contains lightbulb $L_1$ before returning to the battery.

(A)Switch $S_1$ is open and switch $S_2$ is closed.(B)Switch $S_1$ is closed and switch $S_2$ is closed.(C)Switch $S_1$ is open and switch $S_2$ is open.(D)Switch $S_1$ is closed and switch $S_2$ is open.

11. [Skill: 1.4 | Topic: 3.2] A student is investigating a simple circuit consisting of a battery, a single resistor $R_1$, and a switch. The student intends to measure the potential difference across the resistor using an ideal voltmeter. However, the student mistakenly connects the voltmeter in series with the resistor and the battery, rather than in parallel across the resistor. Which of the following best describes the behavior of the circuit compared to its behavior before the voltmeter was added?

(A)The current in the circuit will increase because the voltmeter provides an additional path for the charge to flow.(B)The current in the circuit will decrease to nearly zero because an ideal voltmeter has a very high resistance.(C)The bulb (resistor) will shine brighter because the voltmeter increases the total potential difference in the loop.(D)The circuit will short-circuit, potentially damaging the battery, because the voltmeter has negligible resistance.

12. [Skill: 6.B | Topic: 3.3] A cylindrical wire of length $L$ and diameter $d$ has an electrical resistance $R$. The wire is then stretched uniformly until its length becomes $2L$ while its volume remains constant. What is the new resistance of the wire in terms of $R$?

(A)$R/2$(B)$R$(C)$2R$(D)$4R$

Refer to the figure below.

13. [Skill: 4.B | Topic: 3.3] [Image Cue]: Line graph, Current vs. Potential Difference, The graph shows two lines starting at the origin. Line A is a straight line with a steep slope. Line B is a curve that starts with the same slope as Line A but bends downward toward the voltage axis as potential difference increases. A student collects data for two different circuit elements, A and B, and plots the current $I$ as a function of the potential difference $\Delta V$ across each element as shown in the graph. Which of the following statements is correctly supported by the data?

(A)Element A is non-ohmic because its resistance is represented by the constant slope of the line.(B)Element B is ohmic because the current increases as the potential difference increases.(C)The resistance of Element B increases as the potential difference increases.(D)At a given potential difference, Element A has a higher resistance than Element B.

14. [Skill: 5.A | Topic: 3.3] Two resistors are made of the same material and are held at the same temperature. Resistor 1 is a solid cylinder with length $L$ and radius $r$. Resistor 2 is a solid cylinder with length $2L$ and radius $2r$. Which of the following correctly compares the resistivity $\rho$ and the resistance $R$ of the two resistors?

(A)$\rho_1 = \rho_2$ and $R_1 = R_2$(B)$\rho_1 = \rho_2$ and $R_1 = 2R_2$(C)$\rho_1 = \frac{1}{2}\rho_2$ and $R_1 = R_2$(D)$\rho_1 = \rho_2$ and $R_1 = \frac{1}{2}R_2$

15. [Skill: 1.4 | Topic: 3.4] A battery with a constant potential difference $\Delta V$ is connected in series to two identical light bulbs, each with resistance $R$. The total power dissipated by the circuit is $P_s$. The bulbs are then reconnected in parallel to the same battery, and the total power dissipated by the circuit is $P_p$. What is the ratio $P_p / P_s$? (A) $1/4$ (B) $1/2$ (C) $2$ (D) $4$

(A)1/4(B)1/2(C)2(D)4

Refer to the figure below.

16. [Skill: 2.2 | Topic: 3.4] [Image Cue]: A data table showing measurements for a specific circuit component: Potential Difference $\Delta V = 6.0\text{ V}$, Current $I = 0.50\text{ A}$, and Resistance $R = 12\text{ }\Omega$. A student collects the data shown above for a resistor in a steady-state DC circuit. At what rate is electrical energy being converted into thermal energy by this resistor? (A) $3.0\text{ W}$ (B) $6.0\text{ W}$ (C) $12\text{ W}$ (D) $36\text{ W}$

(A)3.0 W(B)6.0 W(C)12 W(D)36 W

Refer to the figure below.

17. [Skill: 6.4 | Topic: 3.4] [Image Cue]: Circuit diagram consisting of a battery connected to Bulb A. Bulb A is in series with a parallel combination of Bulb B and Bulb C. All bulbs are identical. In the circuit described, all three light bulbs are initially lit and identical. If Bulb B is removed from its socket, creating an open circuit in that branch, what happens to the brightness of Bulb A and Bulb C? (A) Bulb A becomes dimmer; Bulb C becomes brighter. (B) Bulb A becomes brighter; Bulb C becomes dimmer. (C) Both Bulb A and Bulb C become dimmer. (D) Both Bulb A and Bulb C become brighter.

(A)Bulb A becomes dimmer; Bulb C becomes brighter.(B)Bulb A becomes brighter; Bulb C becomes dimmer.(C)Both Bulb A and Bulb C become dimmer.(D)Both Bulb A and Bulb C become brighter.

18. A circuit is constructed using a $12\text{ V}$ ideal DC voltage source and three resistors: $R_1$, $R_2$, and $R_3$. Resistors $R_2$ and $R_3$ are connected in parallel with each other, and this parallel combination is connected in series with $R_1$ and the voltage source. The resistances are $R_1 = 4.0\text{ }\Omega$, $R_2 = 6.0\text{ }\Omega$, and $R_3 = 12\text{ }\Omega$. What is the total current provided by the voltage source to the circuit?

(A)1.5 A(B)2.0 A(C)3.0 A(D)0.55 A

19. A student measures the terminal voltage of a non-ideal battery. When the battery is connected to a circuit such that it provides a current of $2.0\text{ A}$, the potential difference across its terminals is $10.0\text{ V}$. When the external resistance is adjusted so the battery provides a current of $4.0\text{ A}$, the potential difference across its terminals drops to $6.0\text{ V}$. What are the electromotive force ($\epsilon$) and the internal resistance ($r$) of the battery?

(A)$\epsilon $= 12.0 V, r = 1.0 $\Omega$(B)$\epsilon $= 14.0 V, r = 2.0 $\Omega$(C)$\epsilon $= 16.0 V, r = 3.0 $\Omega$(D)$\epsilon $= 10.0 V, r = 0.5 $\Omega$

20. A complex DC circuit contains several resistors. A student wants to measure the current passing through one specific resistor $R_x$ and the potential difference across it. Which of the following describes the correct connection and ideal properties of the meters required?

(A)An ammeter with very high resistance should be connected in parallel with R_x; a voltmeter with very low resistance should be connected in series with R_x.(B)An ammeter with very low resistance should be connected in series with R_x; a voltmeter with very high resistance should be connected in parallel with R_x.(C)An ammeter with very low resistance should be connected in parallel with R_x; a voltmeter with very high resistance should be connected in series with R_x.(D)An ammeter with very high resistance should be connected in series with R_x; a voltmeter with very low resistance should be connected in parallel with R_x.

21. [Skill: 6.4 | Topic: 3.6] A student constructs a circuit containing a single battery and three resistors connected in a combination of series and parallel. The student uses a voltmeter to measure the potential difference across every component along one specific closed-loop path within the circuit. Which of the following fundamental physics principles best justifies the claim that the algebraic sum of these potential differences must be zero?

(A)Conservation of electric charge, because the total current entering a junction must equal the total current leaving it.(B)Conservation of energy, because the net work done by the conservative electric field on a charge moved around a closed path is zero.(C)Conservation of linear momentum, because the drift velocity of the electrons remains constant in a steady-state circuit.(D)Newton’s second law, because the net force on the charge carriers must be zero for a constant current to be maintained.

Refer to the figure below.

22. [Skill: 2.2 | Topic: 3.6] In the circuit shown, a battery with an electromotive force (EMF) of $\varepsilon_1 = 12\text{ V}$ is connected in a single loop with a second battery $\varepsilon_2 = 4\text{ V}$ and two resistors, $R_1$ and $R_2$. The batteries are oriented such that they attempt to push current in opposite directions. If the potential difference across resistor $R_1$ is measured to be $5\text{ V}$, what is the potential difference across resistor $R_2$? [Image Cue]: Circuit diagram of a single rectangular loop. Starting from the bottom left corner and moving clockwise: A battery $\varepsilon_1$ with the positive terminal facing up, a resistor $R_1$, a battery $\varepsilon_2$ with the positive terminal facing down (opposing $\varepsilon_1$), and a resistor $R_2$ on the bottom wire.

(A)3 V(B)7 V(C)11 V(D)13 V

23. [Skill: 1.A | Topic: 3.7] A student is analyzing a complex circuit and identifies a junction where three conducting wires meet. The student observes that the current entering the junction is always equal to the total current leaving the junction. Which of the following fundamental principles of physics best justifies this observation, known as Kirchhoff's junction rule?

(A)The conservation of energy, because the electric potential must be the same for all paths leaving the junction.(B)The conservation of electric charge, because charge cannot build up or be depleted at a point in a steady-state circuit.(C)Newton's third law, because the force exerted by the electrons entering the junction must equal the force of the electrons leaving.(D)Ohm's law, because the current is directly proportional to the potential difference across each branch of the junction.

Refer to the figure below.

24. [Skill: 6.C | Topic: 3.7] [Image Cue]: Circuit diagram showing a single junction labeled $J$. Four wires, $W_1$, $W_2$, $W_3$, and $W_4$, meet at $J$. Arrows indicate the direction of conventional current: $I_1 = 5.0\text{ A}$ flows toward $J$; $I_2 = 2.0\text{ A}$ flows away from $J$; $I_3 = 4.0\text{ A}$ flows toward $J$. Wire $W_4$ carries current $I_4$ in an unknown direction. Based on the junction shown in the diagram, what is the magnitude and direction of the current $I_4$ in wire $W_4$?

(A)1.0 A, flowing toward the junction(B)1.0 A, flowing away from the junction(C)7.0 A, flowing toward the junction(D)7.0 A, flowing away from the junction

25. [Skill: 6.B | Topic: 3.7] In a laboratory experiment, a student measures the charge $Q$ passing through a specific wire entering a junction as a function of time $t$. The data shows that $12.0\text{ C}$ of charge enters the junction through this wire every $3.0\text{ s}$. Two other wires exit this junction. If an ammeter placed on one of the exiting wires measures a constant current of $1.5\text{ A}$, what is the current in the second exiting wire?

(A)1.5 A(B)2.5 A(C)4.0 A(D)5.5 A

26. [Skill: 1.4 | Topic: 3.8] A student is given three capacitors with capacitances $C_1 = 3.0\, \mu F$, $C_2 = 6.0\, \mu F$, and $C_3 = 5.0\, \mu F$. The student connects $C_1$ and $C_2$ in series with each other, and then connects this series combination in parallel with $C_3$. What is the equivalent capacitance $C_{eq}$ of the entire network?

(A)2.0 $\mu $F(B)7.0 $\mu $F(C)9.0 $\mu $F(D)14.0 $\mu $F

Refer to the figure below.

27. [Skill: 5.1 | Topic: 3.8] [Image Cue]: Graph of Charge $Q$ vs. Time $t$ for a charging capacitor in an RC circuit. The curve starts at the origin (0,0) and asymptotically approaches a maximum value $Q_{max}$. A capacitor $C$ is connected in series with a resistor $R$ and an ideal battery of emf $\epsilon$. The graph above shows the charge $Q$ on the capacitor as a function of time $t$ after a switch is closed. If the experiment is repeated using the same battery and capacitor, but the resistor is replaced with one having a resistance of $2R$, which of the following describes the change to the graph?

(A)The horizontal asymptote will increase to $2Q_{max}$.(B)The horizontal asymptote will decrease to $0.5Q_{max}$.(C)The time constant $\tau $will double, meaning the capacitor takes more time to reach a specific fraction of its maximum charge.(D)The initial slope of the graph (at t = 0) will double because the current is higher.

28. [Skill: 6.4 | Topic: 3.8] A circuit consists of an ideal battery with voltage $\Delta V$, a switch, and two identical resistors of resistance $R$ connected in series. A capacitor of capacitance $C$ is then connected in parallel with only one of the resistors. The switch is closed at $t = 0$. Which of the following correctly compares the potential difference across the battery-connected resistor, $V_{R1}$, immediately after the switch is closed to its value after the switch has been closed for a long time?

(A)V_{R1} is initially equal to $\Delta $V and decreases to 0.5$\Delta $V after a long time.(B)V_{R1} is initially equal to 0.5$\Delta $V and remains constant over time.(C)V_{R1} is initially equal to 0.5$\Delta $V and increases to $\Delta $V after a long time.(D)V_{R1} is initially equal to $\Delta $V and remains constant because it is in series with the battery.

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