AP Physics 2 Unit 3 Electric Circuits — Conceptual Foundations, Problem-Solving, and RC Transients

Electric current

The rate at which electric charge flows past a point in a circuit (charge is not “used up”).

Current equation (I = ΔQ/Δt)

Defines current as net charge ΔQ passing a cross-section in time Δt: I = ΔQ/Δt.

Conventional current

Current direction defined as the direction positive charge would move; used for circuit rules and sign conventions.

Electron flow

In metal wires, the mobile charges are electrons, so electron drift direction is opposite the conventional current direction.

Drift velocity

The small net average velocity of charge carriers in an electric field, superimposed on their random thermal motion.

Potential difference (voltage)

A difference in electric potential between two points that can drive charge motion; measured in volts (V).

Voltage as energy per charge (ΔV = ΔU/q)

Electric potential difference equals change in electric potential energy per unit charge: ΔV = ΔU/q (1 V = 1 J/C).

Electromotive force (emf, ℰ)

Energy-per-charge supplied by a source (measured in volts); not actually a force despite the name.

Ideal battery

An ideal source that produces a potential rise of +ℰ from the negative terminal to the positive terminal with no internal losses.

Internal resistance (r)

A real battery model component that dissipates energy inside the source, reducing the terminal voltage when current flows.

Terminal voltage (V_terminal = ℰ − Ir)

The external voltage of a real battery under load: V_terminal = ℰ − Ir (drops below ℰ when delivering current).

Electric power

The rate of electrical energy transfer in a circuit element; measured in watts (W).

Power relations (P = IV = I²R = (ΔV)²/R)

Equivalent power formulas: P = IΔV; for resistors, P = I²R and P = (ΔV)²/R.

Resistance

A measure of how strongly a component opposes current for a given potential difference; measured in ohms (Ω).

Ohm’s law (ΔV = IR)

For an ohmic device under constant conditions, the potential difference across it is proportional to current: ΔV = IR.

Ohmic device

A device with (approximately) constant resistance; shows a linear I–V relationship (straight line through the origin).

Non-ohmic device

A device whose I–V relationship is nonlinear (resistance changes with conditions), e.g., diodes or incandescent bulbs.

I–V characteristic curve

A graph of current I versus voltage ΔV used to determine whether a device is ohmic and to find resistance from slope (when linear).

Resistivity (ρ)

A material property describing how strongly the material resists current flow; used in R = ρL/A (units: Ω·m).

Wire resistance (R = ρL/A)

Resistance of a uniform wire depends on material and geometry: R = ρL/A.

Temperature dependence of resistance (metals)

For many metals, higher temperature increases resistivity (and thus resistance) due to increased lattice vibrations and scattering.

Ideal wire

A connecting wire treated as having negligible resistance, so there is essentially no voltage drop along it.

Node

A set of points connected by ideal wire and therefore at the same electric potential.

Reference node (ground)

A chosen node defined as 0 V to serve as the reference for measuring other potentials in the circuit.

Ammeter (series, low resistance)

A current-measuring device placed in series; ideally has negligible resistance so it doesn’t change the circuit current.

Voltmeter (parallel, high resistance)

A voltage-measuring device placed in parallel; ideally has very large resistance so it draws negligible current.

Short circuit

A very low-resistance path that bypasses a component, forcing nearly zero voltage across the bypassed component in the ideal model.

Series resistors

Resistors are in series when the same current must pass through each (no branching between them).

Series equivalent resistance (sum)

For resistors in series, equivalent resistance adds: R_eq = R1 + R2 + R3 + …

Parallel resistors

Resistors are in parallel when they share the same two nodes, so each has the same voltage across it.

Parallel equivalent resistance (reciprocal sum)

For resistors in parallel: 1/Req = 1/R1 + 1/R2 + 1/R3 + … (Req is less than the smallest branch resistor).

Current splits at a junction

At a node with branching paths, total current divides among branches; branch currents add to the total.

Voltage is the same in parallel branches

All components connected across the same two nodes have the same potential difference across them.

Kirchhoff’s junction rule

Conservation of charge in steady state: the sum of currents into a junction equals the sum of currents out.

Kirchhoff’s loop rule

Conservation of energy per charge: around any closed loop, the algebraic sum of potential changes is zero (ΣΔV = 0).

Loop sign convention for resistors

Traversing a resistor in the direction of current gives a potential drop −IR; opposite the current gives a rise +IR.

Loop sign convention for sources

Across an ideal source, going from negative to positive terminal is +ℰ (rise); from positive to negative is −ℰ (drop).

Kirchhoff solving strategy (systems of equations)

Label branch currents, write junction and independent loop equations, then solve the resulting linear system; negative current means the true direction is opposite the guess.

Mesh current (loop-current) method

A Kirchhoff technique assigning currents to loops (meshes) to simplify writing loop equations, especially in multi-loop circuits.

Shared resistor in mesh analysis (I1 − I2)

In a resistor shared by two mesh loops, the actual current through the shared element is the algebraic difference of mesh currents (e.g., I1 − I2).

Capacitor

A device that stores separated charge (equal and opposite on its plates) and stores energy in an electric field.

Capacitance (C = Q/ΔV)

Measure of charge stored per potential difference: C = Q/ΔV; depends on geometry and dielectric, not on current Q value.

Capacitance as geometry/material property

Capacitance is set by plate arrangement and the material between them (dielectric), rather than by how much charge is presently stored.

Energy stored in a capacitor (U = ½C(ΔV)²)

Energy stored in the capacitor’s electric field: U = (1/2)C(ΔV)² (also U = ½QΔV or Q²/(2C)).

Dielectric

An insulating material between capacitor plates that typically increases capacitance by reducing the effective electric field for a given free charge.

Capacitors in parallel (C_eq adds; same voltage)

Parallel capacitors share the same ΔV; equivalent capacitance adds: C_eq = C1 + C2 + C3 + …

Capacitors in series (1/C_eq adds; same charge)

Series capacitors carry the same charge magnitude in steady state; equivalent capacitance: 1/C_eq = 1/C1 + 1/C2 + …

Capacitor voltage continuity

A capacitor’s voltage cannot change instantaneously: VC(0+) = VC(0−), because an instantaneous change would require infinite current.

Capacitor behavior at t = 0+ vs t → ∞

Immediately after switching, an uncharged capacitor acts like a wire (V_C≈0); at long times in DC, a capacitor acts like an open circuit (I→0).

RC circuits (τ = RC; exponential behavior)

In resistor-capacitor circuits, the time constant is τ = RC; voltages/currents change exponentially during charging/discharging, with ~63% rise (or 37% remaining) after one τ.