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RLC Circuits

H3 Physics hub for inductors and RLC circuits: inductance, materials, inductor energy, RL and LC transients, and RLC damping and regimes.

  • GCE A-Level H3 Physics 2027
Learning goals
  • define self-inductance as the ratio of the e.m.f. induced in an electrical circuit / component to the rate of dI change of current causing it and use V = L to solve problems dt
  • show an understanding that mutual inductance is the tendency of an electrical circuit / component to oppose a change in the current in a nearby electrical circuit / component
  • show a qualitative understanding that dielectric materials enhance capacitance, and that dielectric breakdown can occur when the electric field is sufficiently strong (knowledge of the quantitative modification of electric fields in matter through the permittivity is not required)
  • show a qualitative understanding that ferromagnetic materials enhance inductance and that this enhancement is non-linear especially near saturation (knowledge of the quantitative modification of magnetic fields in matter through the permeability is not required)
  • Apply U = ½LI² to the energy stored in an inductor.
  • Derive the expression U = ½LI² for the potential energy stored in an inductor by considering the work done on charges.
  • solve problems using the formulae for the combined inductance of two or more inductors in series and in parallel
  • solve problems involving circuits with resistors, inductors, and sources of constant e.m.f. (includes solving first-order differential equations) [RL series circuits with constant e.m.f. source]
  • solve problems involving circuits with inductors and capacitors only (includes solving second-order differential equations) [LC series circuits without e.m.f. source]
  • solve problems involving circuits with resistors, inductors and capacitors only (candidates are not expected to solve the general second-order differential equations, though they can be asked to verify and use particular solutions). [RLC series circuits without e.m.f. source]

This topic develops the inductor as an energy-storing circuit component, then uses first- and second-order differential equations to model transient and oscillatory circuits.

Choose your route

Start with inductance, then follow the ordered lessons on this hub. Each lesson adds a model needed by the next circuit type.

Start Here

You should already be comfortable with:

Who this hub is for

Use this hub if you can apply Kirchhoff’s laws in steady circuits but need a reliable method for setting up initial conditions, differential equations, time constants, and damping classifications.

How this hub fits the broader H3 track

RLC circuits is the dynamic-systems branch of H3 electromagnetism. The learning path first establishes inductance and material behaviour, then energy storage, and finally progressively richer RL, LC, and RLC models.

Deep-dive lessons

  1. Inductance — define self-inductance, explain mutual inductance, and combine uncoupled ideal inductors.
  2. Dielectrics and Ferromagnetic Materials — explain capacitance and inductance enhancement, breakdown, non-linearity, and saturation qualitatively.
  3. Energy in an Inductor — derive and apply U_L = 1/2 LI².
  4. RL Circuits — derive current growth and decay from a first-order differential equation.
  5. LC Circuits — model ideal electromagnetic oscillations using charge, current, phase, and energy.
  6. RLC Circuits Analysis — classify source-free series responses and verify particular solutions.
Choose the state variable first

Use current I(t) for an RL circuit. Use capacitor charge q(t) for LC and RLC circuits, then obtain current from I = dq/dt. This keeps signs and initial conditions visible.

Revision

Quick Reference
  • Inductor e.m.f.: E_L = -LdI/dt; the component voltage sign depends on the chosen passive convention.
  • Energy stored: U_L = 1/2 LI².
  • RL time constant: τ = L/R.
  • RL growth/decay: I(t) = I_∞(1-e^(-t/τ)) and I(t) = I₀e^(-t/τ).
  • LC natural frequency: ω₀ = 1/square root of LC and T = 2π square root of LC.
  • Source-free series RLC: Ld²q/dt² + Rdq/dt + q/C = 0.
Problem Templates

Transients (RL / LC / RLC)

  1. Identify the state variable: I(t) for RL or q(t) for LC/RLC.
  2. Write the loop equation (KVL) with correct signs.
  3. Apply initial conditions (e.g., I(0), q(0), capacitor voltage continuity).
  4. Match the form:
    • First-order (RL): exponential with time constant τ = L/R.
    • Second-order (RLC): compare R² with 4L/C to classify damping.
Top Exam Traps
  1. Saying an inductor opposes current; it opposes a change in current.
  2. Mixing up I and q (remember I = dq/dt).
  3. Forgetting that capacitor voltage is continuous (no instantaneous jump in V_C).
  4. Using ω₀ = 1/square root of LC as the observed frequency of a damped oscillation without checking the regime.
  5. Applying ideal series/parallel inductance formulae when mutual coupling is significant.

Practice

Practice (Past-Year + Self-Check)
  • Do one RL growth/decay question and extract τ = L/R from a graph.
  • Do one LC question that requires both phase and energy reasoning.
  • Do one RLC classification question by comparing R with the critical resistance.
H3 Paper Map (9814)

Continue learning

Continue to Special Relativity, the final additional H3 topic.

Course and syllabus information
Course
GCE A-Level H3 Physics
Edition
GCE A-Level H3 Physics 2027