Neutron STEM Lab

Capacitors and Inductors Workbench

Learn electric and magnetic energy storage through capacitor and inductor networks, physical geometry, dielectrics, transients, reactance, coupling, and LC resonance.

Capacitors & Inductors: labelled diagrams and key equations for capacitors, inductors, RC circuits, and RL circuits.
Browser-local interactive workspace
Interactive workspace initializes in your browser. Engineering method, assumptions, validation, and references are available below.

Engineering reference

Capacitors & Inductors: theory, method, and sources

This electrical engineering workspace publishes 11 governing equations, 4 stated assumptions, 2 documented boundaries, and 2 sources so the numbers it returns can be checked rather than taken on trust.

Calculations run locallyCalculation & source methodology

How this tool works

Fourteen guided modules connect physical component construction to circuit behavior in time and frequency domains.

Every numerical plot names the measured quantity and unit, and each module explains the engineering meaning of the result.

Typed, restored, imported, and shared values are clamped before calculations and canvas drawing.

Calculators and topics covered

  • capacitors
  • inductors
  • RC circuits
  • RL circuits
  • reactance
  • energy storage
  • mutual inductance
  • capacitance
  • inductance
  • dielectric
  • parallel plate
  • time constant
  • capacitive reactance
  • inductive reactance

Core equations

Q=CVQ = \mathrm{CV}EC=12CV2E_{C} = \frac{1}{2} \mathrm{CV}^{2}C=εAdC = \frac{\varepsilon A}{d}τRC=RC\tau _{RC} = RCiC=C  dvdti_{C} = \frac{C\; dv}{dt}EL=12LI2E_{L} = \frac{1}{2} LI^{2}L≈μN2AℓL \approx \frac{\mu N^{2} A}{\ell}τRL=LR\tau _{RL} = \frac{L}{R}vL=L  didtv_{L} = \frac{L\; di}{dt}M=kL1L2M = k \sqrt{L_{1} L_{2}}f0=12πLCf_{0} = \frac{1}{2 \pi \sqrt{LC}}

Method and assumptions

Assumptions

  • Components are ideal, linear, lumped, and temperature independent.
  • Parallel-plate and solenoid models neglect fringing and leakage.
  • Inductor network formulas assume no mutual coupling unless the mutual-inductance module is used.
  • LC oscillation is lossless.

Limitations and design boundaries

  • Not a substitute for component datasheets, dielectric-breakdown analysis, magnetic saturation analysis, thermal design, SPICE simulation, laboratory measurement, or electrical safety review.
  • Real capacitors have ESR, ESL, leakage, tolerance, aging, and voltage dependence; real inductors have winding resistance, parasitic capacitance, core loss, and saturation.

Sources and references

Primary sources are preferred for ratings, standards, manufacturer data, and externally defined constants.

Source policy
  • Alexander and Sadiku, Fundamentals of Electric CircuitsCapacitor, inductor, transient, and sinusoidal circuit relationships.
  • Griffiths, Introduction to ElectrodynamicsElectric and magnetic field energy and idealized geometry.

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