---
title: "AP Physics 2 Unit 11 Practice Test"
description: "A timed AP Physics 2 Unit 11 (Electric Circuits) practice test in the AP format, drawn from 1,443 multiple-choice questions and 39 FRQs written for the unit. The standard version takes about 88 minutes."
canonical: "https://fiveable.me/ap-physics-2-revised/unit-test/11"
type: "unit-test"
subject: "AP Physics 2"
unit: "Unit 11"
---

# AP Physics 2 Unit 11 Practice Test

## Overview

A timed AP Physics 2 Unit 11 (Electric Circuits) practice test in the AP format, drawn from 1,443 multiple-choice questions and 39 FRQs written for the unit. The standard version takes about 88 minutes.

## Test Format

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

## Unit FRQs by Type

- [FRQ 1 – Mathematical Routines](/ap-physics-2-revised/frqs/mathematical-routines?unit=11): 10 questions
- [FRQ 2 – Translation Between Representations](/ap-physics-2-revised/frqs/translation-between-representations?unit=11): 9 questions
- [FRQ 3 – Experimental Design](/ap-physics-2-revised/frqs/experimental-design?unit=11): 8 questions
- [FRQ 4 – Qualitative/Quantitative Translation](/ap-physics-2-revised/frqs/qualitative-quantitative-translation?unit=11): 12 questions

## Practice Questions

### Question 1

A steady current of $$0.50$$ A flows through a wire for $$2.0$$ minutes. How many electrons pass through a cross-section of the wire during this time interval?

- (A) $$3.8 \times 10^{20}$$ electrons
- (B) $$6.3 \times 10^{18}$$ electrons
- (C) $$1.9 \times 10^{20}$$ electrons
- (D) $$3.1 \times 10^{18}$$ electrons

**Answer: (A)** Calculating total charge $$Q = It = (0.50 \text{ A})(120 \text{ s}) = 60 \text{ C}$$. Then, dividing by elementary charge: $$n = 60 / (1.6 \times 10^{-19}) \approx 3.75 \times 10^{20}$$, rounding to $$3.8 \times 10^{20}$$.

### Question 2

A beam of doubly ionized helium atoms ($$He^{2+}$$) carries a current of $$3.2 \mu A$$. How many ions pass a fixed point in the beam per second?

- (A) $$1.0 \times 10^{13}$$ ions
- (B) $$2.0 \times 10^{13}$$ ions
- (C) $$5.0 \times 10^{12}$$ ions
- (D) $$4.0 \times 10^{12}$$ ions

**Answer: (A)** Calculating charge per second ($$Q = 3.2 \times 10^{-6}$$ C) and dividing by the charge per ion ($$2e = 3.2 \times 10^{-19}$$ C): $$n = (3.2 \times 10^{-6}) / (3.2 \times 10^{-19}) = 1.0 \times 10^{13}$$.

### Question 3

Two identical spheres, A ($$+10 \mu C$$) and B ($$+2.0 \mu C$$), are connected by a thin wire. Charge flows until equilibrium is reached over $$2.0$$ ms. What is the average current in the wire during this process?

- (A) $$2.0$$ mA from sphere A to B
- (B) $$2.0$$ mA from sphere B to A
- (C) $$6.0$$ mA from sphere A to B
- (D) $$6.0$$ mA from sphere B to A

**Answer: (A)** Equilibrium charge is $$(10+2)/2 = +6 \mu C$$. Sphere A changes from $$+10$$ to $$+6$$, losing $$+4 \mu C$$. Current $$I = \Delta Q/\Delta t = 4 \mu C / 2 \text{ ms} = 2.0 \text{ mA}$$. Positive charge flows A to B.

### Question 4

Two conducting spheres are connected by a wire. A steady current of $$2.0 \text{ A}$$ flows through the wire for $$3.0 \text{ s}$$. What is the magnitude of the total charge transferred between the spheres during this interval?

- (A) $$6.00 \text{ C}$$
- (B) $$0.67 \text{ C}$$
- (C) $$1.50 \text{ C}$$
- (D) $$5.00 \text{ C}$$

**Answer: (A)** Using the functional definition of current $$I = \Delta q / \Delta t$$, the total charge transferred is the product of current and time. $$\Delta q = (2.0 \text{ A})(3.0 \text{ s}) = 6.0 \text{ C}$$.

### Question 5

A capacitor of capacitance $$C$$ is initially uncharged. It is connected in series with a resistor $$R$$ and a battery of emf $$\mathcal{E}$$. At a specific instant $$t$$ during the charging process, the charge on the capacitor is $$q$$. Which of the following expressions correctly represents the current $$i$$ in the circuit at this instant?

- (A) $$i = \frac{\mathcal{E}}{R} - \frac{q}{RC}$$
- (B) $$i = \frac{\mathcal{E}}{R} + \frac{q}{RC}$$
- (C) $$i = \frac{\mathcal{E} - q}{RC}$$
- (D) $$i = \frac{\mathcal{E}}{R} - \frac{q}{R}$$

**Answer: (A)** Kirchhoff's loop rule states $$\mathcal{E} - iR - q/C = 0$$. Solving for $$i$$ gives $$iR = \mathcal{E} - q/C$$, which leads to $$i = (\mathcal{E} - q/C)/R = \mathcal{E}/R - q/RC$$.

### Question 6

Two batteries with emfs $$\mathcal{E}_1$$ and $$\mathcal{E}_2$$ (where $$\mathcal{E}_1 > \mathcal{E}_2$$) are connected in a single series loop with two resistors, $$R_1$$ and $$R_2$$. The batteries are oriented such that their positive terminals face each other. Which expression correctly represents the magnitude of the current $$I$$ in the circuit?

- (A) $$I = \frac{\mathcal{E}_1 - \mathcal{E}_2}{R_1 + R_2}$$
- (B) $$I = \frac{\mathcal{E}_1 + \mathcal{E}_2}{R_1 + R_2}$$
- (C) $$I = \frac{\mathcal{E}_1 - \mathcal{E}_2}{R_1 - R_2}$$
- (D) $$I = \frac{\mathcal{E}_1 + \mathcal{E}_2}{R_1 R_2}$$

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

### Question 7

A capacitor with capacitance $$C$$ is discharging through a resistor of resistance $$R$$. At a specific instant, the current in the circuit is $$I$$. Which of the following expressions correctly represents the charge $$q$$ remaining on the capacitor plates at that instant?

- (A) $$q = IRC$$
- (B) $$q = \frac{IR}{C}$$
- (C) $$q = \frac{IC}{R}$$
- (D) $$q = I(R + C)$$

**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: $$q/C - IR = 0$$. Solving for $$q$$ yields $$q = IRC$$.

### Question 8

A circuit contains a battery of emf $$\mathcal{E}$$ and three resistors $$R_1$$, $$R_2$$, and $$R_3$$ connected in series. Which expression correctly represents the potential difference $$\Delta V_2$$ across the resistor $$R_2$$?

- (A) $$\Delta V_2 = \mathcal{E} \left( \frac{R_2}{R_1 + R_2 + R_3} \right)$$
- (B) $$\Delta V_2 = \mathcal{E} \left( \frac{R_1 + R_3}{R_1 + R_2 + R_3} \right)$$
- (C) $$\Delta V_2 = \mathcal{E} \left( \frac{R_2}{R_1 + R_3} \right)$$
- (D) $$\Delta V_2 = \mathcal{E} \left( \frac{R_1 + R_2 + R_3}{R_2} \right)$$

**Answer: (A)** Using Kirchhoff's loop rule, the current is $$I = \mathcal{E} / (R_1 + R_2 + R_3)$$. The voltage across $$R_2$$ is $$I R_2$$, which substitutes to form the voltage divider equation shown.

### Question 9

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

- (A) $$P_C = I\mathcal{E} - I^2R$$
- (B) $$P_C = I\mathcal{E} + I^2R$$
- (C) $$P_C = I^2R - I\mathcal{E}$$
- (D) $$P_C = \frac{\mathcal{E}^2}{R} - I^2R$$

**Answer: (A)** From the loop rule $$\mathcal{E} = IR + V_C$$, multiplying by $$I$$ gives the power equation $$I\mathcal{E} = I^2R + IV_C$$. The term $$IV_C$$ represents the power delivered to the capacitor ($$P_C$$), so $$P_C = I\mathcal{E} - I^2R$$.

### Question 10

Two capacitors with capacitances $$C_1$$ and $$C_2$$ are connected in series with a battery of emf $$\mathcal{E}$$. Which expression correctly represents the potential difference $$V_1$$ across capacitor $$C_1$$ after the circuit reaches steady state?

- (A) $$V_1 = \mathcal{E} \left( \frac{C_2}{C_1 + C_2} \right)$$
- (B) $$V_1 = \mathcal{E} \left( \frac{C_1}{C_1 + C_2} \right)$$
- (C) $$V_1 = \mathcal{E} \left( \frac{C_1 + C_2}{C_2} \right)$$
- (D) $$V_1 = \mathcal{E} \left( \frac{C_1 C_2}{C_1 + C_2} \right)$$

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

## Review the Unit

- [11.1 Electric Current](/ap-physics-2-revised/unit-11/1-electric-current/study-guide/QaFR8etPqRmh5pdg)
- [11.2 Simple Circuits](/ap-physics-2-revised/unit-11/2-simple-circuits/study-guide/LROjr9EJ6hjfPDMC)
- [11.3 Resistance, Resistivity, and Ohm's Law](/ap-physics-2-revised/unit-11/3-resistance-resistivity-and-ohms-law/study-guide/y0ZmKqhOPqeLWZFa)
- [11.4 Electric Power](/ap-physics-2-revised/unit-11/4-electric-power/study-guide/XlqNl6VwuwtsWe2m)
- [11.5 Compound Direct Current (DC) Circuits](/ap-physics-2-revised/unit-11/5-compound-direct-current-dc-circuits/study-guide/FHwqGLM27UrWSc6A)
- [11.6 Kirchhoff's Loop Rule](/ap-physics-2-revised/unit-11/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN)
- [11.7 Kirchhoff's Junction Rule](/ap-physics-2-revised/unit-11/7-kirchhoffs-junction-rule/study-guide/MhZEtEmvXABB5nTQ)
- [11.8 Resistor-Capacitor (RC) Circuits](/ap-physics-2-revised/unit-11/8-resistor-capacitor-rc-circuits/study-guide/Bzx859T2I32htsAl)

## Other Unit Tests

- [Unit 9: Thermodynamics](/ap-physics-2-revised/unit-test/9)
- [Unit 10: Electric Force, Field, and Potential](/ap-physics-2-revised/unit-test/10)
- [Unit 12: Magnetism and Electromagnetism](/ap-physics-2-revised/unit-test/12)
- [Unit 13: Geometric Optics](/ap-physics-2-revised/unit-test/13)
- [Unit 14: Waves, Sound, and Physical Optics](/ap-physics-2-revised/unit-test/14)
- [Unit 15: Modern Physics](/ap-physics-2-revised/unit-test/15)

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