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AP Course

AP Physics C: Electricity and Magnetism

Updated for the AP Physics C: Electricity and Magnetism framework effective fall 2024, with calculus-based fields, circuits, and induction.

Build calculus-based E&M with original field models, derivations, experiments, quizzes, and practice sets.

Lessons
Electric Charge and Electric ForceConservation of Electric Charge and the Process of ChargingElectric FieldsElectric Fields of Charge DistributionsElectric FluxGauss’s LawElectric Potential EnergyElectric PotentialConservation of Electric EnergyElectrostatics with ConductorsRedistribution of Charge between ConductorsCapacitorsDielectricsElectric CurrentSimple CircuitsResistance, Resistivity, and Ohm’s LawElectric PowerCompound Direct Current CircuitsKirchhoff’s Loop RuleKirchhoff’s Junction RuleResistor Capacitor (RC) CircuitsMagnetic FieldsMagnetism and Moving ChargesMagnetic Fields of Current-Carrying Wires and the Biot-Savart LawAmpère’s LawMagnetic FluxElectromagnetic InductionInduced Currents and Magnetic ForcesInductanceCircuits with Resistors and Inductors (LR Circuits)Circuits with Capacitors and Inductors (LC Circuits)
Quizzes
Practice Problems Formula notes, diagrams, and practice sets will be added here.

AP Physics C: Electricity and Magnetism · Unit 11 · Topic 11.1

Electric Current

Differential equations and conservation rules predict steady and transient behavior in resistive-capacitive networks.

1. Topic Lens

Electric Current is studied through electric circuits. Connect the system boundary, interacting parts, and measurable evidence before applying a formula.

\[I=\frac{dQ}{dt}\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

  1. For a charging loop, Kirchhoff's rule gives ℰ-IR-Q/C=0.
  2. Use I=dQ/dt to form R dQ/dt+Q/C=ℰ.
  3. Solving the first-order equation with Q(0)=0 gives Q=Cℰ(1-e^{-t/RC}) and V=Q/C.
\[V_C(t)=\mathcal E\left(1-e^{-t/RC}\right)\]

3. Detailed Visual Model

Pixel diagram for Electric CurrentOriginal schematic connecting Electric Current to Electric Circuits.
Electric Current: an original pixel-style model. Use it as a schematic, not a literal scale drawing.

4. Worked Example and Lab Link

For R=2 MΩ and C=3 μF, find the time constant.

Answer: τ=RC=(2×10⁶)(3×10⁻⁶)=6 s.

Investigation idea: Collect capacitor voltage versus time, linearize the exponential, and estimate R or C with uncertainty.

Common trap: At one time constant a charging capacitor reaches about 63%, not 100%, of its final voltage.

Checkpoint · Topic 11.1

Explain how electric current supports or limits this conclusion: τ=RC=(2×10⁶)(3×10⁻⁶)=6 s.

Official curriculum reference: College Board AP Physics C: Electricity and Magnetism course page. The explanation and worked example are independently written for this study site.