What it covers: Charges in motion — current, resistance, Ohm's law, series and parallel circuits, Kirchhoff's rules, and capacitors in circuits (including RC circuits).
Exam weight: About 15–18% of the AP Physics 2 exam — tied for the highest-weighted unit.
The big question: How do voltage, current, and resistance interact to determine the behavior of a circuit, no matter how complex?
In the College Board CED: Unit 11: Electric Circuits (Topics 11.1–11.8) — the revised CED numbers Physics 2 units 9–15.
Key topics at a glance
Electric Current
I = ΔQ/Δt. Conventional current flows in the direction positive charge would move, even though electrons (negative) physically move the other way in metals.
Resistance & Ohm's Law
V = IR. Resistance depends on material and geometry: R = ρL/A. Longer/thinner wires resist more; shorter/thicker wires resist less.
Electric Power
P = IV = I²R = V²/R. The rate at which electrical energy converts to heat, light, or other forms in a circuit element.
Series Circuits
Same current everywhere. R_eq = R1 + R2 + ... Voltage divides across components proportional to resistance.
Parallel Circuits
Same voltage across every branch. 1/R_eq = 1/R1 + 1/R2 + ... Current divides inversely with resistance.
Kirchhoff's Rules
Junction rule: current in = current out (charge conservation). Loop rule: voltage changes around any loop sum to zero (energy conservation).
Capacitors in DC Circuits
Uncharged capacitor = momentary short (max current). Fully charged capacitor = open circuit (zero current through that branch).
RC Circuits
τ = RC. Charge, current, and voltage change exponentially over time rather than instantly — the signature behavior of resistor-capacitor combinations.
The key terms you must know
Electric current (I = ΔQ/Δt) — the rate of charge flow through a conductor, measured in amperes.
Ohm's law (V = IR) — the relationship between voltage, current, and resistance for an ohmic resistor.
Resistivity (ρ) — an intrinsic material property used to calculate resistance via R = ρL/A.
Series vs. parallel — series shares current and divides voltage; parallel shares voltage and divides current.
Kirchhoff's junction and loop rules — charge conservation and energy conservation applied to circuit analysis.
EMF and internal resistance — the energy per charge a battery supplies, reduced by its own internal resistance when current flows.
RC time constant (τ = RC) — the characteristic timescale for exponential charging/discharging behavior.
Key themes to remember
Series and parallel rules are mirror images of each other. What adds directly in series (resistance) divides reciprocally in parallel, and vice versa for capacitance.
Kirchhoff's rules are just conservation laws in disguise. The junction rule is charge conservation; the loop rule is energy conservation. Nothing new — just applied to circuits.
Capacitors fight change, not current itself. They resist sudden changes in voltage, which is why they act like wires when uncharged and like open switches once fully charged.
Exponential behavior shows up whenever a quantity's rate of change depends on its own current value. RC charging/discharging is the AP Physics 2 example of this broader pattern.
Redraw the circuit before calculating anything. Identifying which elements are truly in series vs. parallel is often the hardest — and most important — first step.
Common exam traps
Don't average resistors in parallel — use the reciprocal formula. Equivalent parallel resistance is always less than the smallest resistor, never an average.
Adding a resistor in parallel decreases total resistance; adding one in series increases it. A common mix-up under exam pressure.
EMF and terminal voltage aren't the same once current flows. Terminal voltage = EMF − I×(internal resistance); they're equal only when no current flows (open circuit).
A capacitor's behavior depends on time, not just connection. Right after connecting (uncharged) it acts like a wire; after a long time (fully charged) it acts like an open circuit — don't assume one or the other without checking the timing.
Capacitors in series combine like resistors in parallel, and vice versa. This swap is one of the most common AP Physics 2 mix-ups.
The time constant τ = RC doesn't represent "the time to fully charge." It's the time to reach about 63% of the way to full charge (or 37% remaining when discharging) — full charging takes much longer in practice.