Electric Circuits — AP Physics 2 Unit Overview

For: AP Physics 2 candidates sitting AP Physics 2.

Covers: The full scope of the AP Physics 2 Electric Circuits unit, including all 5 core sub-topics: circuit definitions, resistivity, Ohm’s and Kirchhoff’s rules, conservation of charge, and steady-state DC RC circuit analysis.

You should already know: Basic properties of electric charge. Electric potential and potential difference. Coulomb’s law and electrostatics fundamentals.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Physics 2 style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. Why This Unit Matters

Electric Circuits is one of the highest-weighted units in AP Physics 2, making up 20% of total exam points per the official College Board CED, appearing in both multiple-choice and free-response sections. This unit moves beyond abstract electrostatics to apply core physics principles to real-world systems we interact with daily: phone batteries, medical sensors, home power grids, and wearable electronics. It reinforces two of the AP Physics 2 big ideas: conservation of energy and conservation of charge, framing these abstract laws in a concrete, calculable context. Mastery of this unit is non-negotiable for success on the exam, and it acts as a prerequisite for all subsequent topics involving applied electromagnetism, including electromagnetic induction and AC circuits. Unlike electrostatics, which focuses on stationary charge, this unit teaches you to predict the behavior of moving charge in controlled paths, building problem-solving skills that transfer to nearly every other unit in the course.

2. Unit Concept Map

The 5 sub-topics of this unit build sequentially from foundational language to complex circuit analysis, with each step relying completely on mastery of the previous. The first sub-topic, Definition of a Circuit, establishes the core language and notation: it defines open vs closed circuits, series vs parallel connections, emf vs terminal voltage, and standard circuit symbols. Without this shared vocabulary, you cannot even correctly interpret what a circuit problem is asking. Next, Resistivity and Resistance builds on basic circuit definitions to connect the physical properties of a conductor (length, cross-sectional area, material) to its ability to impede current flow, introducing the relationship between resistance and resistivity that you will use for all circuit calculations. Third, Ohm's Law, Kirchhoff's Loop Rule and Power ties resistance and potential difference to current flow, and applies conservation of energy to closed circuits to derive the loop rule, the first core analytical tool for any circuit. Fourth, Kirchhoff's Junction Rule and Conservation of Charge extends conservation principles to moving charge, adding the second core rule needed to analyze multi-loop circuits with multiple current branches. Finally, Steady-State DC Circuits with Resistors and Capacitors combines all previous rules to analyze circuits with energy-storing components, explaining how capacitors behave when fully charged or uncharged in steady-state conditions.

3. Guided Tour of a Full Unit Problem

We will walk through a single exam-style problem to show how multiple sub-topics are used in sequence to solve it:

Problem: A 12 V ideal battery is connected to a 2 Ω resistor in series with a parallel branch. One branch of the parallel network has a 4 Ω resistor; the other branch holds a 10 μF capacitor that has reached steady state after being connected for an hour. Find the total current drawn from the battery and the total charge stored on the capacitor.

Step 1: Use Definition of a Circuit to parse the problem: First, confirm connection topology: the 2 Ω resistor is in series with a parallel combination, so current flows through the 2 Ω then splits into two branches. The problem specifies an "ideal battery", so we know it has zero internal resistance, and terminal voltage equals emf. Step 2: Apply rules from Steady-State DC Circuits with Resistors and Capacitors: In steady state, a fully charged capacitor acts as an open circuit, so no current flows through the capacitor’s branch. This immediately simplifies the circuit: only the 4 Ω resistor in the parallel branch carries current. Step 3: Use Ohm's Law, Kirchhoff's Loop Rule to find total resistance and current: The 2 Ω resistor is in series with the 4 Ω resistor, so total equivalent resistance is $R_{eq}=2\Omega +4\Omega =6\Omega$. By Ohm’s law, total current drawn from the battery is $I=V/R_{eq}=12V/6\Omega =2A$. Step 4: Use Kirchhoff's Junction Rule and Conservation of Charge to find the voltage across the capacitor: All current flows through the 4 Ω resistor, so the voltage drop across the 2 Ω resistor is $V_2=IR=2A\times 2\Omega =4V$. By Kirchhoff’s loop rule, the sum of voltages around the loop is zero, so the voltage across the parallel branch (and thus across the open capacitor) is $V_C=12V-4V=8V$. The charge on the capacitor is $Q=C{V}_C=10\times 10^{-6}F\times 8V=80\mu C$.

Exam tip: Always apply steady-state capacitor rules before doing any other calculations. Simplifying the circuit by removing open capacitor branches cuts the problem’s complexity in half before you start algebra.

4. Cross-Cutting Common Pitfalls

• Wrong move: Treating a capacitor in a steady-state DC circuit as a zero-resistance conductor, so calculating non-zero current through it. Why: Confuses the instantaneous behavior of an uncharged charging capacitor with its steady-state behavior, mixing rules from different sub-topics. Correct move: Always note if the problem asks for steady-state DC; immediately mark all capacitor branches as open (no current) before any other calculations.
• Wrong move: Adding resistances in parallel the same way as series: $R_{eq}=R_1+R_2$. Why: Memorizes formulas without first confirming connection topology, relying on the first sub-topic’s definitions incorrectly. Correct move: Always trace current paths first: if current splits into multiple separate paths, it is parallel (use reciprocal sum); if current flows through one resistor then the next with no split, it is series (add directly).
• Wrong move: Ignoring a battery’s given internal resistance, using emf instead of terminal voltage for calculations. Why: Confuses emf (total energy per charge supplied by the battery) with terminal voltage (actual potential difference across the battery terminals when current flows), a core definition mix-up. Correct move: Always check if the problem gives an internal resistance; if it does, add it to your total series equivalent resistance at the start of your calculation.
• Wrong move: Applying Kirchhoff’s loop rule with inconsistent signs: adding voltage drops across resistors as positive when traversing the loop against the current. Why: Fails to consistently apply sign conventions rooted in core potential difference definitions. Correct move: Before summing, mark all potential gains (negative to positive across a battery, against current across a resistor) as positive, and all potential drops as positive, then set the total sum to zero.
• Wrong move: Calculating power for an individual resistor using the battery’s total emf instead of the voltage drop across the individual resistor. Why: Confuses total circuit values with local component values, failing to apply Ohm’s law at the component level. Correct move: For any individual component, always use the current through that component and the voltage across that component for all calculations, never total circuit values unless the component is the only one in the circuit.

5. Quick Check: Do You Know When To Use Each Sub-Topic?

For each scenario below, identify which sub-topic(s) you would use to answer:

1. A copper wire of length 2 m and diameter 1 mm has 1.5 V across its ends. Find the current flowing through the wire.
2. A multi-loop circuit with three batteries and five resistors has unknown currents in each branch. Find all unknown currents.
3. What is the equivalent resistance of three resistors where current from the battery splits evenly across all three before recombining?
4. Find the maximum charge stored on a capacitor connected to a battery for 12 hours.

6. Practice Questions (AP Physics 2 Style)

Question 1 (Multiple Choice)

A fully charged capacitor is placed in a steady-state DC circuit in parallel with a 10 Ω resistor connected to a 9 V ideal battery. What is the current through the capacitor? A) 0 A B) 0.9 A C) 90 A D) Cannot be determined without knowing the capacitance

Worked Solution: In steady-state DC, a fully charged capacitor has a potential difference equal to the potential difference across its branch, so no net charge flows onto or off of the capacitor’s plates. This means the current through the capacitor is zero, regardless of its capacitance. The 0.9 A value is the current through the parallel resistor, not the capacitor, so option B is incorrect. The correct answer is A.

Question 2 (Free Response)

A non-ideal 12 V battery has an internal resistance of 0.5 Ω. It is connected to a 1.5 Ω resistor in series with a parallel combination of a 3 Ω resistor and a 6 Ω resistor. (a) Calculate the total equivalent resistance of the entire circuit, including the battery's internal resistance. (b) Calculate the total current drawn from the battery, and the terminal voltage of the battery. (c) Calculate the total power dissipated by the external resistors.

Worked Solution: (a) First find the equivalent resistance of the parallel branch: $$\frac{1}{R_{par}}=\frac{1}{3\Omega }+\frac{1}{6\Omega }=\frac{2+1}{6}=\frac{1}{2}⟹R_{par}=2\Omega$$ Add the series 1.5 Ω external resistor and 0.5 Ω internal resistance: $$R_{total}=0.5+1.5+2=4.0\Omega$$

(b) Use Ohm’s law for total current: $$I_{total}=\frac{V_{emf}}{R_{total}}=\frac{12V}{4\Omega }=3A$$ Terminal voltage equals emf minus voltage drop across internal resistance: $$V_{term}=12V-(3A\times 0.5\Omega )=10.5V$$

(c) Total power dissipated by external resistors is equal to the power supplied to the external circuit, calculated as: $$P=V_{term}{I}_{total}=10.5V\times 3A=31.5W$$

Question 3 (Real-World Application)

A portable power bank is rated for a 5.0 V open-circuit output and has an internal resistance of 0.2 Ω. When charging a tablet that draws 1.8 A of steady current, what is the terminal voltage output by the power bank? If the power bank stores 20 Wh of total energy, how long can it sustain this current output?

Worked Solution: First calculate the voltage drop across the power bank’s internal resistance: $$V_{drop}=Ir=1.8A\times 0.2\Omega =0.36V$$ Terminal voltage is open-circuit emf minus internal drop: $$V_t=5.0V-0.36V=4.64V$$ Total output power is $P=V_{t}I=4.64V\times 1.8A=8.35W$. Time to drain the 20 Wh battery is: $$t=\frac{20Wh}{8.35W}\approx 2.4hours$$ This means the power bank can charge the tablet continuously for roughly 2 and a half hours at this current draw before being fully exhausted.

7. Quick Reference Cheatsheet

8. What's Next and See Also

After mastering this unit, you will move on to magnetic fields and electromagnetic induction, where you will analyze induced currents in circuits. The ability to quickly calculate equivalent resistance, apply Ohm’s law, and use Kirchhoff’s rules is required to solve any induction problem that asks for induced current or power, so this unit is a critical prerequisite. This unit also lays the groundwork for college-level circuit analysis, including dynamic RC transients and AC circuits. The core conservation principles you practice here transfer to other AP Physics 2 topics, including fluid flow and thermal energy transfer.

Deep dives for each sub-topic in this unit:

• Definition of a Circuit
• Resistivity and Resistance
• Ohm's Law, Kirchhoff's Loop Rule and Power
• Kirchhoff's Junction Rule and Conservation of Charge
• Steady-State DC Circuits with Resistors and Capacitors