Electric Circuits

Name: AP Physics 2: Algebra-Based Unit 3: Electric Circuits
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15–18% of the exam7 lessons · 96 min47 terms

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What this unit covers

The topics below follow the published Physics 2 course framework for Unit 3. This unit is worth 15–18% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Current & resistanceSeries & parallelRC circuitsKirchhoff’s rules

Lessons in this unit

Formulas in Unit 3

Current, Ohm’s law, and power

I = Q / t · V = I · R · P = I · V = I² · R = V² / R

Power P is the rate at which the resistor converts electrical energy to heat/light, in watts (W). All three power forms are equivalent — pick the one matching your known quantities.

Combining resistors

Series: R = R₁ + R₂ + … · Parallel: 1/R = 1/R₁ + 1/R₂ + …

Series total is bigger than any part; parallel total is smaller than any part. For two parallel resistors, a handy shortcut is R = (R₁R₂)/(R₁ + R₂).

Kirchhoff’s rules

Junction: ΣI_in = ΣI_out · Loop: ΣΔV = 0

Going through a resistor in the direction of current is a voltage drop (−IR); passing from − to + inside a battery is a rise (+EMF). Reverse the sign if you traverse against that direction.

Capacitor charge and RC time constant

Q = C · V · τ = R · C

The time constant τ (tau), in seconds, sets the pace of charging: after one τ the capacitor reaches about 63% of full charge, and after ~5τ it is essentially fully charged. Larger R or C means slower charging.

Choosing the form

same CURRENT (series) → use P = I²R, so larger R dissipates MORE · same VOLTAGE (parallel) → use P = V²/R, so larger R dissipates LESS

The two conclusions are opposite. This is why "does a bigger resistor dissipate more power?" has no answer until you know how it is connected.

The two rules you expand with

SERIES: current is the same, voltages add · PARALLEL: voltage is the same, currents add

Every step of the expansion phase uses one of these. Naming which one you are using prevents applying the wrong one.

Terminal voltage and total current

V_terminal = ε − Ir · with an external resistance R: I = ε / (R + r)

Internal resistance adds in series with everything else. It is why a battery gets warm under heavy load and why terminal voltage sags.

Every term in Unit 3

All 47 terms we publish for Electric Circuits, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.

Current: I = ΔQ/Δt, the rate of charge flow in amperes. Conventional current is defined as positive charge flow, opposite to actual electron motion.
Resistance and resistivity: R = ρL/A. A longer wire has more resistance and a thicker one has less; resistivity is the material property behind both.
Ohm's law: V = IR. Holds for ohmic materials at constant temperature; a filament bulb is non-ohmic because resistance rises as it heats.
Electrical power: P = IV = I²R = V²/R. Which form to use depends on which two quantities you know.
Series resistors: R_total = ΣR. Same current through each; voltage divides in proportion to resistance.
Parallel resistors: 1/R_total = Σ(1/R). Same voltage across each; total resistance is always less than the smallest branch.
Kirchhoff's junction rule: Current into a junction equals current out — a statement of charge conservation.
Kirchhoff's loop rule: Potential changes around any closed loop sum to zero — a statement of energy conservation.
Capacitance: C = Q/V in farads. For parallel plates, C = ε₀A/d, so larger plates or a smaller gap store more charge per volt.
Energy stored in a capacitor: U = ½QV = ½CV² = Q²/2C. All three forms are equivalent; pick the one matching your known quantities.
Capacitors in series and parallel: Reciprocals add in SERIES and capacitances add in PARALLEL — the opposite of resistors. Charging a capacitor stores U = ½CV².
Dielectric: An insulator between the plates that reduces the field for the same charge, raising capacitance by the dielectric constant.
RC circuit charging: Charge and voltage rise exponentially toward their final values with time constant τ = RC; current starts maximum and decays.
Capacitor behavior at t = 0 and t = ∞: Initially uncharged, a capacitor acts like a wire; fully charged, it acts like a break in the circuit.
Internal resistance and terminal voltage: A real battery has internal resistance, so terminal voltage V = ε − Ir falls as current increases.
Reading a circuit diagram: Identify which components share both nodes (parallel) and which carry the same current (series) before writing any equation.
Brightness reasoning: Brightness tracks dissipated power. In series the same current flows, so the larger resistance is brighter; in parallel the same voltage applies, so the smaller resistance is brighter.
Effect of adding a parallel branch: Lowers total resistance, raising total current drawn from the source and increasing the voltage lost to internal resistance.
Measuring resistance experimentally: Plot V against I; the slope is resistance. A curved plot means the component is non-ohmic.
Why ammeters must have low resistance: They carry the circuit current, so any appreciable resistance would change the very quantity being measured.
Capacitor charging graph: Voltage rises with a decreasing slope toward the source value while current decays exponentially from its initial maximum.
Energy dissipated during capacitor charging: Exactly half the energy supplied by the battery ends up stored; the other half is dissipated in the resistance, regardless of its value.
Series vs parallel capacitor voltage: In series each capacitor carries the same charge and the smallest capacitance takes the largest voltage share.
Kirchhoff sign conventions: A potential drop across a resistor traversed with the current, a rise crossing a battery from negative to positive terminal.
Three forms of power: P = IV = I²R = V²/R. All always true; which one makes a comparison easy depends on what is shared.
Choosing the power form: Same CURRENT (series) → P = I²R, so larger R dissipates MORE. Same VOLTAGE (parallel) → P = V²/R, so larger R dissipates LESS. Opposite conclusions.
Brightness in series versus parallel: Series: the higher-resistance bulb is brighter. Parallel: the lower-resistance bulb is brighter. Memorizing one case gets the other backward.
Removing a bulb: Series: everything goes out. Parallel: the others are unaffected. Mixed: removing a parallel branch raises total resistance, lowering current and dimming series elements.
Kilowatt-hour: One kilowatt for one hour, 3.6 × 10⁶ J. A device rated in watts at a stated voltage has implied resistance R = V²/P.
Collapse then expand: Reduce the innermost clearly-series or clearly-parallel group to one resistor, repeat to a single value, then work back out using the two rules at each stage.
What "in parallel" actually requires: Both ends connected to the SAME pair of nodes — not merely drawn side by side. A wire with no component is one node however long.
Parallel sanity check: The equivalent is always SMALLER than the smallest member. If it came out larger, you added resistances instead of reciprocals.
Forgetting the final reciprocal: Computing 1/12 + 1/4 = 1/3 and reporting 1/3 Ω instead of 3 Ω. The smaller-than-smallest check catches it immediately.
emf versus terminal voltage: emf ε is a fixed property. Terminal voltage is ε − Ir, so it falls as current rises. They coincide only at zero current.
Why headlights dim when cranking: The starter draws huge current, so the Ir drop inside the battery is large and terminal voltage sags. An aged battery has higher r and can read healthy unloaded.
Ideal ammeter: Near-ZERO resistance, connected in SERIES. Otherwise it changes the current it is measuring.
Ideal voltmeter: Near-INFINITE resistance, connected in PARALLEL. Otherwise it draws current and reduces the voltage it reports.
Meters connected wrongly: Ammeter in parallel is a short circuit and usually destroys the meter. Voltmeter in series nearly stops the current and reads almost nothing.
Internal resistance is in series: Add it to the external resistance BEFORE computing current. Computing I from R alone and subtracting afterward gives too large a current.
Kirchhoff junction rule: Current in equals current out at every junction — conservation of charge. The basis of every branch-current calculation.
Kirchhoff loop rule: Potential differences around any closed loop sum to zero — conservation of energy. Track signs by walking the loop consistently.
Conventional current direction: Defined as the direction positive charge would flow, so it runs opposite to the actual electron drift. Every circuit rule uses the conventional direction.
Resistivity versus resistance: R = ρL/A. Resistivity is a material property; resistance also depends on the geometry, so a longer or thinner wire of the same material has more resistance.
Why a capacitor blocks steady current: Once fully charged it carries no current, so in a DC steady state it behaves as a break in the circuit. Immediately after switching, it behaves as a short.
RC time constant: τ = RC, the time to reach about 63% of the final charge. After about 5τ the capacitor is effectively fully charged.
Capacitors combine backward from resistors: Capacitances ADD in parallel and reciprocals add in series — the opposite of resistors, because a parallel capacitor adds plate area.
Where the energy goes: Every joule the battery supplies is either dissipated as heat in resistances, including the battery internal resistance, or stored in a capacitor field.

What examiners penalize here

Know all three power formulas: P = IV, P = I²R, and P = V²/R. If a problem gives you resistance and voltage but not current, P = V²/R saves a step. They are algebraically identical via Ohm’s law.
Anchor each rule with its shared quantity: series shares current, parallel shares voltage. From that, use V = IR branch by branch. Complex networks reduce to one equivalent resistor by collapsing series and parallel groups one step at a time.
Pair the rules with their conservation law: junction rule = conservation of charge, loop rule = conservation of energy. On multi-loop problems, write one junction equation and one loop equation per unknown current, then solve the system.
For RC problems, answer three questions: what happens at t = 0 (capacitor = wire), what happens as t → ∞ (capacitor = open, fully charged with Q = CV), and how fast (τ = RC). Those three checkpoints capture nearly every exam item.
Before ranking power, write down whether the elements share current or share voltage. That one line determines which expression to use and therefore which direction the ranking goes.
Write the equivalent resistance at every stage of the collapse and keep those values — you need them on the way back out. Discarding intermediate results means recomputing them, which is where time is lost on circuit free responses.
When a question distinguishes "emf" from "terminal voltage", it is testing internal resistance. Write V = ε − Ir explicitly rather than treating the two as the same number — the distinction is usually the point of the question.

Practice Physics 2

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

194 practice questionsEvery one with a written explanation FRQ trainerWritten answers scored against the rubric Physics 2 study guideAll units, weights and score data in one place All 7 Physics 2 unitsThe full course

Questions about this unit

How much of the AP Physics 2: Algebra-Based exam is Unit 3?

Unit 3, Electric Circuits, is worth 15–18% of the Physics 2 multiple-choice section according to the published course framework. Across all 7 units that makes it a substantial share — heavier than an even split would give it.

What topics are covered in Physics 2 Unit 3?

Electric Circuits covers Current & resistance, Series & parallel, RC circuits and Kirchhoff’s rules. We publish 47 terms with definitions for this unit, all of them on this page.

How should I study Physics 2 Unit 3?

Read the 7 lessons below first — about 95 minutes — then drill the 47 terms in cram mode until you can produce each definition from memory rather than just recognize it. Recognition is what makes a unit feel finished when it is not. Finish with practice questions and read the explanation for every one you get right by elimination as well as the ones you miss.

All 7 units of AP Physics 2: Algebra-Based

Unit names, topics and exam weights follow the published College Board course framework for AP Physics 2: Algebra-Based. AP® is a trademark registered by the College Board, which does not endorse this site.