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AP Physics 2 Unit 11 practice questions

Try 10 multiple-choice questions from Unit 11 here. Pick an answer to see why it's right or wrong, then take the timed test above for a full AP-style set.

  1. Question 1

    A capacitor of capacitance CC is initially uncharged. It is connected in series with a resistor RR and a battery of emf E\mathcal{E}. At a specific instant tt during the charging process, the charge on the capacitor is qq. Which of the following expressions correctly represents the current ii in the circuit at this instant?

    i=ER−qRCi = \frac{\mathcal{E}}{R} - \frac{q}{RC}

    i=ER+qRCi = \frac{\mathcal{E}}{R} + \frac{q}{RC}

    i=E−qRCi = \frac{\mathcal{E} - q}{RC}

    i=ER−qRi = \frac{\mathcal{E}}{R} - \frac{q}{R}

    Show answer

    Answer: (A)

    Kirchhoff's loop rule states E−iR−q/C=0\mathcal{E} - iR - q/C = 0. Solving for ii gives iR=E−q/CiR = \mathcal{E} - q/C, which leads to i=(E−q/C)/R=E/R−q/RCi = (\mathcal{E} - q/C)/R = \mathcal{E}/R - q/RC.

  2. Question 2

    Two batteries with emfs E1\mathcal{E}_1 and E2\mathcal{E}_2 (where E1>E2\mathcal{E}_1 > \mathcal{E}_2) are connected in a single series loop with two resistors, R1R_1 and R2R_2. The batteries are oriented such that their positive terminals face each other. Which expression correctly represents the magnitude of the current II in the circuit?

    I=E1−E2R1+R2I = \frac{\mathcal{E}_1 - \mathcal{E}_2}{R_1 + R_2}

    I=E1+E2R1+R2I = \frac{\mathcal{E}_1 + \mathcal{E}_2}{R_1 + R_2}

    I=E1−E2R1−R2I = \frac{\mathcal{E}_1 - \mathcal{E}_2}{R_1 - R_2}

    I=E1+E2R1R2I = \frac{\mathcal{E}_1 + \mathcal{E}_2}{R_1 R_2}

    Show answer

    Answer: (A)

    Kirchhoff's loop rule sums the potential changes: a rise through E1\mathcal{E}_1, a drop through E2\mathcal{E}_2 (since they oppose), and drops through both resistors. Thus E1−E2−I(R1+R2)=0\mathcal{E}_1 - \mathcal{E}_2 - I(R_1 + R_2) = 0, which solves to this expression.

  3. Question 3

    A capacitor with capacitance CC is discharging through a resistor of resistance RR. At a specific instant, the current in the circuit is II. Which of the following expressions correctly represents the charge qq remaining on the capacitor plates at that instant?

    q=IRCq = IRC

    q=IRCq = \frac{IR}{C}

    q=ICRq = \frac{IC}{R}

    q=I(R+C)q = I(R + C)

    Show answer

    Answer: (A)

    According to Kirchhoff's loop rule for a discharging circuit, the potential difference across the capacitor must equal the potential drop across the resistor: q/C−IR=0q/C - IR = 0. Solving for qq yields q=IRCq = IRC.

  4. Question 4

    A circuit contains a battery of emf E\mathcal{E} and three resistors R1R_1, R2R_2, and R3R_3 connected in series. Which expression correctly represents the potential difference ΔV2\Delta V_2 across the resistor R2R_2?

    ΔV2=E(R2R1+R2+R3)\Delta V_2 = \mathcal{E} \left( \frac{R_2}{R_1 + R_2 + R_3} \right)

    ΔV2=E(R1+R3R1+R2+R3)\Delta V_2 = \mathcal{E} \left( \frac{R_1 + R_3}{R_1 + R_2 + R_3} \right)

    ΔV2=E(R2R1+R3)\Delta V_2 = \mathcal{E} \left( \frac{R_2}{R_1 + R_3} \right)

    ΔV2=E(R1+R2+R3R2)\Delta V_2 = \mathcal{E} \left( \frac{R_1 + R_2 + R_3}{R_2} \right)

    Show answer

    Answer: (A)

    Using Kirchhoff's loop rule, the current is I=E/(R1+R2+R3)I = \mathcal{E} / (R_1 + R_2 + R_3). The voltage across R2R_2 is IR2I R_2, which substitutes to form the voltage divider equation shown.

  5. Question 5

    In a circuit loop, a battery of emf E\mathcal{E} drives current II through a resistor RR and charges a capacitor CC. Which of the following expressions represents the rate at which energy is being stored in the electric field of the capacitor?

    PC=IE−I2RP_C = I\mathcal{E} - I^2R

    PC=IE+I2RP_C = I\mathcal{E} + I^2R

    PC=I2R−IEP_C = I^2R - I\mathcal{E}

    PC=E2R−I2RP_C = \frac{\mathcal{E}^2}{R} - I^2R

    Show answer

    Answer: (A)

    From the loop rule E=IR+VC\mathcal{E} = IR + V_C, multiplying by II gives the power equation IE=I2R+IVCI\mathcal{E} = I^2R + IV_C. The term IVCIV_C represents the power delivered to the capacitor (PCP_C), so PC=IE−I2RP_C = I\mathcal{E} - I^2R.

  6. Question 6

    Two capacitors with capacitances C1C_1 and C2C_2 are connected in series with a battery of emf E\mathcal{E}. Which expression correctly represents the potential difference V1V_1 across capacitor C1C_1 after the circuit reaches steady state?

    V1=E(C2C1+C2)V_1 = \mathcal{E} \left( \frac{C_2}{C_1 + C_2} \right)

    V1=E(C1C1+C2)V_1 = \mathcal{E} \left( \frac{C_1}{C_1 + C_2} \right)

    V1=E(C1+C2C2)V_1 = \mathcal{E} \left( \frac{C_1 + C_2}{C_2} \right)

    V1=E(C1C2C1+C2)V_1 = \mathcal{E} \left( \frac{C_1 C_2}{C_1 + C_2} \right)

    Show answer

    Answer: (A)

    In series, charge QQ is the same for both. V1=Q/C1V_1 = Q/C_1 and V2=Q/C2V_2 = Q/C_2. Loop rule: E=V1+V2\mathcal{E} = V_1 + V_2. Substituting and solving for V1V_1 yields this inverse relationship (voltage divides inversely to capacitance).

  7. Question 7

    A single loop circuit contains a battery of emf E\mathcal{E}, a resistor RR, and a switch. When the switch is open, no current flows. Which expression correctly represents the potential difference VsV_s across the open switch terminals?

    Vs=EV_s = \mathcal{E}

    Vs=E−VRV_s = \mathcal{E} - V_R

    Vs=0V_s = 0

    Vs=E/2V_s = \mathcal{E}/2

    Show answer

    Answer: (A)

    Applying Kirchhoff's loop rule to the open circuit: E−IR−Vs=0\mathcal{E} - IR - V_s = 0. Since the switch is open, I=0I = 0, so the term IRIR vanishes, leaving Vs=EV_s = \mathcal{E}.

  8. Question 8

    A variable resistor RR is connected in series with a battery of emf E\mathcal{E} and internal resistance rr. Which expression represents the power PP dissipated by the variable resistor in terms of the given quantities?

    P=E2R(R+r)2P = \mathcal{E}^2 \frac{R}{(R + r)^2}

    P=E2RR2+r2P = \mathcal{E}^2 \frac{R}{R^2 + r^2}

    P=E21R+rP = \mathcal{E}^2 \frac{1}{R + r}

    P=E2r(R+r)2P = \mathcal{E}^2 \frac{r}{(R + r)^2}

    Show answer

    Answer: (A)

    First, derive current using the loop rule: I=E/(R+r)I = \mathcal{E} / (R + r). Then, substitute this into the power equation P=I2RP = I^2 R to get P=[E/(R+r)]2RP = [\mathcal{E} / (R + r)]^2 R, which matches the correct expression.

  9. Question 9

    Two resistors R1R_1 and R2R_2 are connected in parallel. This combination is connected in series with a battery of emf E\mathcal{E} and a third resistor R3R_3. Which expression represents the current I3I_3 flowing through resistor R3R_3?

    I3=ER3+R1R2R1+R2I_3 = \frac{\mathcal{E}}{R_3 + \frac{R_1 R_2}{R_1 + R_2}}

    I3=ER3+R1+R2I_3 = \frac{\mathcal{E}}{R_3 + R_1 + R_2}

    I3=ER3+R1+R2R1R2I_3 = \frac{\mathcal{E}}{R_3 + \frac{R_1 + R_2}{R_1 R_2}}

    I3=E(R1+R2)R1R2R3I_3 = \frac{\mathcal{E} (R_1 + R_2)}{R_1 R_2 R_3}

    Show answer

    Answer: (A)

    Kirchhoff's loop rule requires finding the total equivalent resistance. The parallel combination is Rp=(R1R2)/(R1+R2)R_p = (R_1 R_2)/(R_1 + R_2). The total resistance is R3+RpR_3 + R_p. The total current I3I_3 is E/Rtotal\mathcal{E} / R_{total}.

  10. Question 10

    A battery of emf E\mathcal{E} is connected to a resistor RR and an uncharged capacitor CC in series. Which expression represents the voltage VRV_R across the resistor at the exact moment the circuit is closed (t=0t=0)?

    VR=EV_R = \mathcal{E}

    VR=0V_R = 0

    VR=E/2V_R = \mathcal{E} / 2

    VR=E(1−e−1)V_R = \mathcal{E} (1 - e^{-1})

    Show answer

    Answer: (A)

    At t=0t=0, the uncharged capacitor has q=0q=0, so the potential drop across it (VC=q/CV_C = q/C) is zero. By Kirchhoff's loop rule, E−VR−0=0\mathcal{E} - V_R - 0 = 0, so VR=EV_R = \mathcal{E}.

What's on the AP Physics 2 Unit 11 practice test

The standard version takes about 88 minutes and follows the timing and directions of the AP exam, sized to one unit:

  • 20 Multiple Choice Questions (40 minutes)
  • 1 FRQ – FRQ 1 – Mathematical Routines (24 minutes)
  • 1 FRQ – FRQ 2 – Translation Between Representations (24 minutes)

Questions are drawn from 1443 multiple-choice questions and 39 FRQs written for Unit 11, Electric Circuits.

Practice AP Physics 2 Unit 11 FRQs

Answer the unit's free-response questions one at a time and get a score on every part.

Review Unit 11 before you start

Other AP Physics 2 unit tests