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RC, RL and RLC Circuits Course

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Engineering, Construction and Technology

Electricity

RC, RL and RLC Circuits Course

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RC, RL and RLC Circuits Course

Master the analysis and design of RC, RL, and RLC circuits from DC fundamentals through advanced frequency response and resonance. This course takes you from Ohm's law and Kirchhoff's laws all the way to second-order transient responses, phasor analysis, and practical filter design. Build the circuit analysis skills that engineers use every day.

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What you will learn:

You will start with core DC circuit laws and work through capacitor and inductor behavior, first-order transient responses, and AC steady-state analysis using phasors and complex impedance. From there, you will tackle second-order RLC circuits, classify overdamped and underdamped responses, and analyze resonance in series and parallel configurations. You will derive transfer functions, sketch Bode plots, and design low-pass, high-pass, bandpass, and notch filters. Advanced topics include impedance matching networks, LC oscillators, SPICE simulation, and parasitic effects in real circuits. By the end, you will have a complete, systematic toolkit for analyzing and designing circuits across both time and frequency domains.

How you study in practice RC, RL and RLC Circuits Course

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Course Content

8 Chapters • 39 LessonsDuration between 4 and 360 hours (you decide)

Chapter 1See details

Fundamentals of Electrical Circuits

Lesson 1 • Kirchhoff's Voltage and Current Laws
Presents KVL and KCL as universal conservation principles for circuit analysis. Enables systematic equation writing for any network topology.
Lesson 2 • Series and Parallel Resistor Networks
Derives equivalent resistance formulas for series and parallel combinations. Provides tools to simplify complex resistive networks before analysis.
Lesson 3 • Ohm's Law and Power
Applies Ohm's law to relate voltage, current, and resistance in resistive elements. Introduces power dissipation as a practical design constraint.
Lesson 4 • DC Sources and Circuit Theorems
Introduces ideal and practical voltage and current sources. Covers Thevenin and Norton equivalents to reduce complex circuits to simple models.
Lesson 5 • Voltage, Current, and Resistance
Defines the three core electrical quantities and their units. Establishes the physical intuition needed for all subsequent circuit analysis.

Chapter 2See details

Capacitors and Inductors: Energy Storage

Lesson 1 • Initial and Final Conditions
Defines initial conditions for capacitor voltage and inductor current at switching instants. Correct initial conditions are essential for solving transient circuit equations.
Lesson 2 • Inductor Fundamentals
Explains inductance, magnetic flux linkage, and the v-i relationship involving the time derivative of current. Establishes duality with capacitor behavior.
Lesson 3 • Practical Component Characteristics
Addresses real-world non-idealities such as equivalent series resistance and parasitic inductance. Bridges ideal models to components used in actual circuit design.
Lesson 4 • Capacitor Fundamentals
Explains capacitance, the parallel-plate model, and the i-v relationship involving the time derivative of voltage. Connects physical structure to circuit behavior.

Chapter 3See details

First-Order RC Circuit Transient Analysis

Lesson 1 • Step Response of RC Circuits
Solves for capacitor voltage when a DC step input is applied. Demonstrates the complete response as the sum of natural and forced components.
Lesson 2 • Energy Analysis in RC Transients
Calculates energy stored, delivered, and dissipated during RC transients. Reinforces conservation of energy as a verification tool for circuit solutions.
Lesson 3 • Pulse and Switched RC Circuits
Extends transient analysis to circuits with switches and pulsed inputs by applying the general solution sequentially. Covers practical timing and waveform shaping applications.
Lesson 4 • General Solution Method for RC Circuits
Presents the unified formula v(t) = v(∞) + [v(0) − v(∞)]e^(−t/τ) for any RC circuit. Streamlines analysis by identifying three key quantities.
Lesson 5 • Natural Response of RC Circuits
Derives the exponential decay of capacitor voltage when a charged capacitor discharges through a resistor. Introduces the time constant τ = RC as the key parameter.

Chapter 4See details

First-Order RL Circuit Transient Analysis

Lesson 1 • Inductive Voltage Spikes and Protection
Explains the large voltage spike generated when inductor current is interrupted suddenly. Introduces flyback diodes and snubber circuits as practical protection methods.
Lesson 2 • Step Response of RL Circuits
Solves for inductor current growth when a DC voltage is applied. Identifies forced and natural components of the complete response.
Lesson 3 • Energy Analysis in RL Transients
Quantifies energy stored in the inductor and energy dissipated in the resistor during RL transients. Confirms energy conservation across the complete transient interval.
Lesson 4 • Natural Response of RL Circuits
Derives the exponential decay of inductor current when the source is removed. Establishes τ = L/R and contrasts RL behavior with RC duality.
Lesson 5 • General Solution Method for RL Circuits
Applies the unified formula i(t) = i(∞) + [i(0) − i(∞)]e^(−t/τ) to any RL circuit. Parallels the RC general method for consistent problem-solving strategy.

Chapter 5See details

AC Steady-State Analysis and Phasors

Lesson 1 • Impedance of R, L, and C Elements
Derives complex impedance for resistors, inductors, and capacitors in the phasor domain. Unifies all three elements under a single algebraic framework.
Lesson 2 • Phasor Representation of Sinusoids
Transforms sinusoidal time-domain signals into complex phasors using Euler's formula. Enables algebraic manipulation of AC quantities instead of differential equations.
Lesson 3 • AC Circuit Analysis Techniques
Applies KVL, KCL, voltage divider, and Thevenin methods in the phasor domain. Demonstrates that all DC analysis techniques extend directly to AC phasor circuits.
Lesson 4 • AC Power: Real, Reactive, and Apparent
Defines real power, reactive power, apparent power, and power factor for AC circuits. Connects power concepts to practical energy efficiency and load management.
Lesson 5 • Sinusoidal Signals and Parameters
Defines amplitude, frequency, period, phase angle, and RMS value of sinusoidal waveforms. Establishes the mathematical form used throughout AC analysis.

Chapter 6See details

Second-Order RLC Circuit Analysis

Lesson 1 • Second-Order Circuit Equations
Formulates the second-order ODE for series and parallel RLC circuits from KVL and KCL. Identifies the characteristic equation and its role in determining response type.
Lesson 2 • Step Response of RLC Circuits
Adds a DC forcing function to the homogeneous solution to find the complete step response. Covers all three damping cases with initial condition application.
Lesson 3 • Damping Ratio and Component Selection
Relates damping ratio ζ and natural frequency ω_n to R, L, and C values. Enables engineers to design circuits with specified transient performance.
Lesson 4 • Overdamped and Critically Damped Responses
Solves the second-order ODE when roots are real and distinct or repeated. Interprets the physical meaning of slow, non-oscillatory transient behavior.
Lesson 5 • Underdamped Response and Oscillation
Solves for complex conjugate roots producing damped sinusoidal oscillations. Defines damped natural frequency and envelope decay rate.

Chapter 7See details

Frequency Response and Resonance

Lesson 1 • Series RLC Resonance
Analyzes the series RLC circuit at resonance where inductive and capacitive reactances cancel. Derives resonant frequency, impedance minimum, and current maximum.
Lesson 2 • Parallel RLC Resonance and Bandpass Filters
Analyzes parallel RLC resonance where admittance is minimized and impedance is maximized. Extends resonance concepts to bandpass and band-reject filter design.
Lesson 3 • RC and RL Filter Responses
Derives low-pass and high-pass transfer functions for RC and RL circuits. Identifies cutoff frequency and the −3 dB point as key filter specifications.
Lesson 4 • Bode Plot Construction
Constructs asymptotic Bode magnitude and phase plots using straight-line approximations. Provides a rapid graphical tool for visualizing filter behavior across decades.
Lesson 5 • Transfer Functions and Frequency Response
Defines the transfer function H(jω) as the ratio of output to input phasors. Establishes magnitude and phase response as functions of frequency.

Chapter 8See details

Advanced RLC Circuit Design and Applications

Lesson 1 • Impedance Matching Networks
Uses L-networks and pi-networks built from reactive elements to match source and load impedances. Maximizes power transfer in RF and audio circuit applications.
Lesson 2 • Coupled Inductors and Transformers
Introduces mutual inductance, coupling coefficient, and the transformer as a coupled-inductor circuit. Analyzes voltage and current transformation ratios.
Lesson 3 • LC and RLC Oscillator Circuits
Analyzes the conditions for sustained oscillation in LC tank circuits and RLC feedback oscillators. Connects resonance theory to practical signal generation.
Lesson 4 • Simulation and Measurement of RLC Circuits
Applies SPICE-based simulation and bench measurement techniques to verify RLC circuit designs. Bridges theoretical analysis with practical laboratory validation.
Lesson 5 • Filter Design Using RLC Circuits
Translates frequency-response specifications into component values for low-pass, high-pass, bandpass, and band-reject filters. Covers both series and parallel topologies.

Certification

Your valid completion certificate

This course is for you:

Electrical engineering students: needing a stronger grip on reactive circuit behavior.
Electronics technicians: ready to move beyond troubleshooting into principled circuit analysis.
Embedded hardware developers: building confidence with analog circuits around their microcontrollers.
Hobbyists and makers: wanting to design circuits intentionally rather than by trial and error.
Career changers entering electronics: seeking a rigorous but accessible technical foundation.
Mechanical or software engineers: expanding into electrical design for multidisciplinary projects.

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