AP Physics C: Electricity and Magnetism Unit 4 Practice Test & Exam | 24 Questions

Questions 1-3 refer to the following circuit.

1. What is the magnitude of the current flowing through the resistor?

(A)0.25 A(B)3.0 A(C)4.0 A(D)36 A

2. At what rate is energy dissipated as heat in the resistor?

(A)4 W(B)12 W(C)36 W(D)48 W

3. If the 3 Ω resistor is replaced by a 6 Ω resistor, which of the following correctly describes the effect on the circuit?

(A)The current is doubled, and the power dissipated is doubled.(B)The current is doubled, and the power dissipated is halved.(C)The current is halved, and the power dissipated is halved.(D)The current is halved, and the power dissipated is doubled.

Questions 4-6 refer to the following circuit diagram.

4. What is the equivalent resistance of the entire circuit?

(A)3.0 Ω(B)7.0 Ω(C)9.0 Ω(D)21 Ω

5. What is the current flowing through the 3 Ω resistor?

(A)2.0 A(B)3.0 A(C)6.0 A(D)9.0 A

6. Let $I6$ be the current through the 6 Ω resistor and $I{12}$ be the current through the 12 Ω resistor. Which of the following statements is correct?

(A)$I6 = I{12}$ because they are in the same circuit.(B)$I6 = 2 I{12}$ because the potential difference across them is the same.(C)$I{12} = 2 I6$ because the potential difference across them is the same.(D)$I6 = I{12}$ because they are in parallel.

7. Which equation correctly represents an application of Kirchhoff's junction rule to the top junction?

(A)$I1 + I2 + I_3 = 0$(B)$I1 + I2 = I_3$(C)$I1 = I2 + I_3$(D)$I3 = I1 - I_2$

8. Which equation correctly represents an application of Kirchhoff's loop rule for a clockwise path around the left loop?

(A)$10 - 2I1 - 5I3 = 0$(B)$10 - 2I1 + 5I3 = 0$(C)$10 + 2I1 + 5I3 = 0$(D)$-10 - 2I1 - 5I3 = 0$

9. Kirchhoff's junction rule and loop rule are derived from which fundamental conservation principles, respectively?

(A)Conservation of energy; conservation of charge(B)Conservation of charge; conservation of energy(C)Conservation of momentum; conservation of charge(D)Conservation of charge; conservation of momentum

Questions 10-12 refer to the following information and graph.

10. Which of the following physical quantities is represented by the slope of the graph at any time $t$?

(A)The current in the circuit(B)The potential difference across the resistor(C)The energy stored in the capacitor(D)The time constant of the circuit

11. Immediately after the switch is closed (at $t=0^+$), which of the following is true?

(A)The current is zero, and the potential difference across the capacitor is $\mathcal{E}$.(B)The current is at its maximum value, and the potential difference across the capacitor is zero.(C)The current is at its maximum value, and the potential difference across the capacitor is $\mathcal{E}$.(D)The current is zero, and the potential difference across the capacitor is zero.

12. After the switch has been closed for a very long time ($t \to \infty$), what is the potential difference across the resistor?

(A)$\mathcal{E}$(B)$\mathcal{E}/2$(C)$\mathcal{E}/e$(D)Zero

13. A copper wire of length $L$ and cross-sectional area $A$ has resistance $R$. A second copper wire has a length of $2L$ and a cross-sectional area of $A/2$. What is the resistance of the second wire?

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

14. A cylindrical resistor of length $L$ and cross-sectional area $A$ is made of a material whose resistivity varies along its length according to the function $\rho(x) = \rho_0 (1 + x/L)$, where $x$ is the distance from one end. Which of the following integrals correctly gives the total resistance of the resistor?

(A)$R = \int{0}^{L} \frac{\rho0(1+x/L)}{A} dx$(B)$R = \int{0}^{L} \rho0(1+x/L) A dx$(C)$R = \int{0}^{L} \frac{A}{\rho0(1+x/L)} dx$(D)$R = \frac{\rho0}{A} \int{0}^{L} x dx$

15. A real battery has an emf of $\mathcal{E} = 9.0$ V and an internal resistance of $r = 0.5 \Omega$. When the battery is connected to an external resistor $R$, a current of $1.5$ A flows. What is the terminal voltage of the battery?

(A)0.75 V(B)8.25 V(C)9.0 V(D)9.75 V

16. Two identical lightbulbs, Bulb 1 and Bulb 2, are connected to an ideal battery. First, they are connected in series. Then, they are reconnected in parallel. How does the brightness of Bulb 1 in the parallel connection compare to its brightness in the series connection?

(A)It is one-quarter as bright.(B)It is half as bright.(C)It is twice as bright.(D)It is four times as bright.

17. A student wants to measure the current through and the potential difference across a resistor $R$ in a simple circuit. How should an ideal ammeter and an ideal voltmeter be connected?

(A)The ammeter in series with $R$; the voltmeter in series with $R$.(B)The ammeter in parallel with $R$; the voltmeter in parallel with $R$.(C)The ammeter in series with $R$; the voltmeter in parallel with $R$.(D)The ammeter in parallel with $R$; the voltmeter in series with $R$.

18. The current density $\vec{J}$ in a wire is defined as $\vec{J} = nq\vec{v}d$, where $n$ is the charge carrier density, $q$ is the charge of each carrier, and $\vec{v}d$ is the drift velocity of the carriers. If the radius of a cylindrical wire is doubled while the total current $I$ remains constant, what happens to the magnitude of the drift velocity $v_d$?

(A)It is quadrupled.(B)It is doubled.(C)It is halved.(D)It is quartered.

19. Three capacitors are connected as shown. What is the equivalent capacitance between points X and Y?

(A)1.5 µF(B)3.0 µF(C)5.5 µF(D)12 µF

20. A student makes the following statement: "In a simple series circuit with a battery and a lightbulb, the current is largest when it leaves the battery and gets used up by the lightbulb, so the current returning to the battery is smaller." Which of the following best describes this statement?

(A)The statement is correct because the lightbulb consumes charge.(B)The statement is correct because the lightbulb dissipates energy.(C)The statement is incorrect because charge is conserved, so the current is the same at all points in the series circuit.(D)The statement is incorrect because energy is conserved, so the current must be the same at all points in the series circuit.

Refer to the figure below.

21. The graph below shows the electric potential $V$ as a function of position $x$ around a single-loop circuit containing an ideal battery and two resistors, $R1$ and $R2$. The loop starts and ends at point A. Based on the graph, which of the following is true?

(A)The emf of the battery is 8 V.(B)The potential drop across $R1$ is greater than the potential drop across $R2$.(C)The resistance of $R1$ is less than the resistance of $R2$.(D)The current is not constant throughout the circuit.

22. In a circuit containing a battery with emf $\mathcal{E}$, a resistor $R$, and a capacitor $C$, Kirchhoff's loop rule is applied while the capacitor is charging. Which of the following differential equations correctly describes the charge $q$ on the capacitor as a function of time $t$?

(A)$\mathcal{E} - \frac{dq}{dt}R - \frac{q}{C} = 0$(B)$\mathcal{E} - \frac{dq}{dt}R + \frac{q}{C} = 0$(C)$\mathcal{E} - I^2R - \frac{q^2}{2C} = 0$(D)$\mathcal{E} - \frac{d^2q}{dt^2}R - \frac{q}{C} = 0$

23. In the circuit shown, the switch S is initially open. When the switch is closed, what happens to the equivalent resistance of the circuit and the total current supplied by the battery?

(A)Equivalent resistance decreases; total current decreases.(B)Equivalent resistance decreases; total current increases.(C)Equivalent resistance increases; total current decreases.(D)Equivalent resistance increases; total current increases.

24. A current $I$ flows through a resistor $R$, causing a potential difference $\Delta V$ across it and dissipating power $P$. If the current through the resistor is tripled to $3I$, what is the new power dissipated by the resistor, assuming it is an ohmic resistor? Section II: Free-Response Time:45 minutes 4 Questions Directions:Show all your work. Credit for your answers depends on the clarity with which you justify them and the correctness of your work. FRQ 1[Skills: Mathematical Routines, Argumentation | Topics: 4.5, 4.6, 4.7, 4.4] The circuit shown above consists of an ideal 24 V battery and three resistors with resistances $R1 = 4 \Omega$, $R2 = 6 \Omega$, and $R_3 = 12 \Omega$. The switch S is initially open. i. Does the total current supplied by the battery increase, decrease, or stay the same? _ Increase _ Decrease _ Stay the same ii. Justify your answer. i. The equivalent resistance of the circuit. ii. The total current supplied by the battery. FRQ 2[Skills: Experimental Methods, Data Analysis, Representation | Topic: 4.3] A group of students is tasked with determining the resistivity $\rho$ of a long, thin wire made of an unknown material. They are provided with the following equipment: | Length $L$ (m) | Current $I$ (A) | | :--- | :--- | | 0.20 | 2.50 | | 0.40 | 1.25 | | 0.60 | 0.83 | | 0.80 | 0.63 | | 1.00 | 0.50 | The students must calculate the resistance $R$ for each length. On the axes below, plot a graph of Resistance $R$ versus Length $L$. Draw a best-fit line for the data. FRQ 3[Skills: Derivation, Mathematical Routines | Topic: 4.8] In the circuit shown above, the components have the following values: $\mathcal{E} = 12$ V, $R = 2.0 \times 10^6 \Omega$, and $C = 3.0 \mu$F. The switch S is initially open and the capacitor is uncharged. At time $t=0$, the switch is closed. FRQ 4[Skills: Argumentation, Comparison, Mathematical Routines | Topic: 4.4] Two identical, ideal batteries are used in two different circuits as shown above. All four lightbulbs (A, B, C, and D) are identical, each having a resistance $R$. _ Increases _ Decreases _ Stays the same Justify your answer.

(A)In circuit X, which bulb is brighter, or are they the same brightness? Justify your answer.(B)In circuit Y, which bulb is brighter, or are they the same brightness? Justify your answer.(C)Which bulb is the brightest out of all four bulbs (A, B, C, and D)? Justify your answer by comparing the power dissipated by the bulbs. Your justification should include expressions for the power of a bulb from each circuit in terms of the battery emf $\mathcal{E}$ and the resistance $R$.(D)If bulb D in Circuit Y burns out (creating an open circuit in its branch), what happens to the brightness of bulb C?

AP Physics C: Electricity and Magnetism Unit 4: Electric Circuits Practice Exam

Exam Details

A. Multiple-Choice Questions (24 Questions)

AP Physics C: Electricity and Magnetism Unit 4: Electric Circuits Practice Exam

Exam Details

A. Multiple-Choice Questions (24 Questions)