AP Physics C E&M Full Mock Test 3 — Circuits, RC Differential Equations, and Kirchhoff Analysis

About Full Mock 3

Full Mock 3 for AP Physics C: Electricity & Magnetism places its most demanding questions on electric circuit analysis — Unit 11's Kirchhoff's laws, RC circuit differential equations, and time-constant analysis. While the full 35 MCQ + 3 FRQ format maintains coverage of all six E&M units, this mock builds circuit analysis stamina and differential equation fluency that are tested heavily in real AP-style FRQs.

Circuit Analysis Topics Under Emphasis

Kirchhoff's Laws in Complex Networks

Mock 3 includes multi-loop circuit problems requiring students to define current variables, write KCL equations at junctions, and formulate KVL equations around multiple independent loops. The resulting system of simultaneous linear equations must be solved for individual branch currents. AP-style presentation requires showing the loop equations explicitly before solving — partial credit is awarded for correct equation setup even if algebra contains errors.

RC Circuit Differential Equations

The centrepiece of Mock 3's circuit content is the RC circuit ODE. FRQ problems require:

• Applying KVL to a charging or discharging RC circuit to write the differential equation R(dq/dt) + q/C = ε (or = 0)
• Solving by separation of variables: separating dq and dt, integrating both sides, applying initial conditions
• Expressing the solution as q(t) = Cε(1 − e^(−t/RC)) or q(t) = Q₀e^(−t/RC)
• Differentiating to obtain I(t) = dq/dt and interpreting the sign

Time-Constant Analysis

Multiple MCQ and FRQ sub-parts in Mock 3 test quantitative and qualitative understanding of the time constant τ = RC. Questions include: computing τ for circuits with parallel or series combinations of R and C, sketching q(t) and I(t) with correct initial values and asymptotes labelled, and determining how τ changes when resistance or capacitance values are modified.

Integration with Electrostatics (Units 8–10)

Mock 3 FRQs are designed to embed circuit analysis within broader electrostatics problems. A representative structure: (a) derive the capacitance of a given geometry using Gauss's law, (b) compute the initial charge when connected to a battery, (c) write and solve the RC discharge ODE when the battery is disconnected, (d) sketch I(t) and compute the total charge that flows during discharge. This four-part integration tests Units 8, 10, and 11 in a single coherent FRQ.

Common Errors Targeted in Mock 3

• Using I = q/t (average current) instead of I = dq/dt in the ODE derivation
• Forgetting to apply initial conditions after solving the homogeneous ODE
• Sign errors in KVL around loops — particularly with multiple EMF sources of opposing polarity
• Treating the capacitor as a fixed resistor rather than as a time-varying voltage source q/C in the loop equation