RC, RL and RLC Circuits Course

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 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 behaviour.

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 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 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 behaviour with RC duality.

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 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 behaviour.

Lesson 1 • Series RLC Resonance

Analyses 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

Analyses parallel RLC resonance where admittance is minimised and impedance is maximised. 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 visualising filter behaviour across decades.

Lesson 1 • Impedance Matching Networks

Uses L-networks and pi-networks built from reactive elements to match source and load impedances. Maximises 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. Analyses voltage and current transformation ratios.

Lesson 3 • LC and RLC Oscillator Circuits

Analyses 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.