J. W. Nilsson & S. A. Riedel, Electric Circuits, 12th ed., Pearson, 2023 — Chapters 6–7.
Inductance/capacitance, stored energy, continuity constraints, and systematic first-order RL/RC natural and step responses.
DY-01
Course overview
Capacitors, inductors, RC & RL first-order dynamics
Volume I established circuit laws, sinusoidal analysis and measurement. DY-01 now introduces genuine circuit memory in the time domain. The course begins with the constitutive laws and stored energy of ideal capacitors and inductors, then builds first-order differential equations, natural and step responses of RC/RL networks, and the physical meaning of time constants before reconnecting those dynamics to first-order filtering.
5 chapters5 available · 0 plannedfoundational → intermediate
Prerequisites
- Volume I — circuits, signals, AC & measurement
- Elementary differential calculus
By the end of the course
- Derive time-domain laws and stored energy of C and L.
- Build a first-order circuit differential equation from Kirchhoff laws.
- Solve RC natural and step responses.
- Solve RL natural and step responses.
- Interpret time constants, initial/final conditions and the link to first-order filtering.
Syllabus
Five readings from energy storage to first-order RC/RL responses.
Volume I established circuit laws, sinusoidal analysis and measurement. DY-01 now introduces genuine circuit memory in the time domain. The course begins with the constitutive laws and stored energy of ideal capacitors and inductors, then builds first-order differential equations, natural and step responses of RC/RL networks, and the physical meaning of time constants before reconnecting those dynamics to first-order filtering.
- 01→
Capacitors, inductors & stored energy
Build the two ideal energy-storage elements from their time-domain constitutive laws before solving any transient circuit. Derive q=Cv and i=C dv/dt for a linear capacitor, v=L di/dt for a linear inductor, integrate power to obtain wC=½Cv² and wL=½Li², prove the ideal continuity of capacitor voltage and inductor current under finite excitation, distinguish state from instantaneous power flow, and mark the physical limits of the lumped ideal models.
150–190 min · Foundational → intermediate · available - 02→
First-order differential equations
Derive the mathematical skeleton shared by one-storage-element linear circuits before specializing to RC or RL. Reduce Kirchhoff plus one constitutive law to a first-order linear ODE, derive natural and forced response by integrating factor, show the equivalent final-value form x(t)=x∞+[x(0+)−x∞]e^(−t/τ), interpret τ as the time for the error to fall by e^(−1), and separate state continuity, initial conditions, final conditions and switching topology into a reusable solution workflow.
155–195 min · Intermediate · available - 03→
RC transients
Specialize the generic first-order framework to linear RC networks. Use capacitor-voltage continuity for the initial state, reduce the post-switch linear resistive network seen by the capacitor to a Thévenin equivalent when valid, derive τ=RthC and vC(t)=v∞+[v0−v∞]e^(−t/τ), obtain current and resistor voltage from the same solution, solve source-free and driven switching examples, and verify endpoints, slopes, energy and dependent-source handling without relying on separate charging/discharging formulas.
165–210 min · Intermediate · available - 04→
RL transients
Apply the same first-order method to one-inductor linear networks. Carry inductor current continuously through switching, reduce the t>0 resistive/source network seen by L, derive L diL/dt+Rth iL=Vth and τ=L/Rth, solve source-free and driven current responses, derive inductor voltage from di/dt, explain why interrupting current can demand a large voltage, verify energy dissipation, and state when ideal one-inductor reasoning fails.
165–210 min · Intermediate · available - 05→
Time constants, poles & first-order filters
Unify the complete first-order picture. Starting from the state response, derive the meaning of one time constant and arbitrary settling thresholds, identify the pole s=−1/τ, derive ωc=1/τ for the normalized first-order pole, prove the exact 10–90% rise-time relation tr=τ ln9 and fc tr≈0.3497, map RC/RL output choices to low-pass/high-pass transfer functions, and show how transient and frequency-response measurements can cross-check the same model without treating −3 dB, five time constants or 0.35 as universal laws.
170–220 min · Intermediate · available
Reference backbone
References used
The course follows the standard undergraduate circuit-theory path used in Nilsson & Riedel, Alexander & Sadiku and Agarwal & Lang/MIT 6.002: energy-storage elements first, then first-order equations and responses. Open educational resources are used for additional worked intuition, but derivations remain anchored in standard circuit laws and energy conservation.
C. K. Alexander & M. N. O. Sadiku, Fundamentals of Electric Circuits — Chapters 6–7.
Capacitor/inductor constitutive laws, energy, first-order circuits, time constants and complete-response methods.
A. Agarwal & J. H. Lang, Foundations of Analog and Digital Electronic Circuits, Morgan Kaufmann, 2005 — energy-storage and first-order-system chapters.
Physical state/memory interpretation and derivation of first-order circuit dynamics from lumped constitutive relations.
MIT OpenCourseWare 6.002 — Capacitors and first-order systems; inductors and first-order step response.
University-level lecture structure and worked intuition connecting capacitor/inductor physics to first-order systems.
All About Circuits, RC and L/R Time Constants.
Open supplementary examples for qualitative charging/discharging intuition and limiting-case checks.
AoN EF-01, DC-02, AC-01 & AC-02.
Prerequisite sign conventions, Kirchhoff laws, constitutive/impedance continuity and frequency-response notation.
MIT OpenCourseWare 2.003 — Lab 5: 1st-order RC circuits and measured step/frequency response.
Independent time-domain versus frequency-domain validation of the same first-order electrical model.