Network Theorems Course

Lesson 1 • Power and Energy in Circuits

Covers power dissipation, delivery, and energy storage in circuit elements. Reinforces conservation principles used in theorem verification.

Lesson 2 • Kirchhoff's Laws

Presents KVL and KCL as the governing conservation laws of circuits. These laws underpin the derivation of every major network theorem.

Lesson 3 • Voltage, Current, and Resistance

Defines the three fundamental electrical quantities and their relationships. Provides the quantitative basis for every theorem introduced later.

Lesson 4 • Circuit Elements and Symbols

Introduces passive and active circuit elements with standard schematic symbols. Connects element behaviour to later theorem-based analysis.

Lesson 1 • Node-Voltage Method

Teaches systematic assignment of node voltages and KCL-based equation writing. Forms the analytical backbone for superposition and Thevenin derivations.

Lesson 2 • Dependent Sources in Systematic Analysis

Extends node and mesh methods to circuits containing dependent sources. Prepares students for Thevenin and Norton analysis with controlled sources.

Lesson 3 • Mesh-Current Method

Introduces mesh currents and KVL-based loop equations for planar circuits. Complements node analysis and simplifies ladder and bridge circuits.

Lesson 4 • Source Transformation Technique

Demonstrates equivalence between voltage-source-series-resistor and current-source-parallel-resistor pairs. Directly supports Thevenin and Norton conversions.

Lesson 1 • Superposition with AC and DC Sources

Extends superposition to circuits mixing DC and sinusoidal AC sources. Previews phasor-domain thinking needed in advanced network analysis.

Lesson 2 • Computing Individual Source Contributions

Applies node, mesh, or inspection methods to each single-source sub-circuit. Builds skill in selecting the most efficient analysis method per sub-circuit.

Lesson 3 • Algebraic Recombination of Responses

Combines individual contributions with correct sign conventions to obtain total response. Reinforces polarity discipline critical for all subsequent theorems.

Lesson 4 • Deactivating Independent Sources

Explains how to suppress voltage and current sources when isolating each source's contribution. Correct deactivation is essential for accurate superposition results.

Lesson 1 • Thevenin Analysis with Dependent Sources

Handles circuits where dependent sources prevent simple source deactivation for Rth. Reinforces test-source and Isc methods as the reliable alternatives.

Lesson 2 • Load Analysis Using Thevenin Equivalent

Uses the Thevenin equivalent to rapidly evaluate circuit behaviour for varying loads. Demonstrates the practical power of the theorem in design contexts.

Lesson 3 • Finding Thevenin Resistance

Covers three methods for computing Rth: source deactivation, test-source injection, and short-circuit current ratio. Method selection depends on source types present.

Lesson 4 • Thevenin Equivalent Concept

Introduces the idea of replacing a complex network with a single voltage source and series resistance. Motivates the theorem through load analysis efficiency.

Lesson 1 • Norton Resistance Determination

Reuses Thevenin resistance methods to find Rn, confirming Rth equals Rn. Reinforces the unified resistance concept across both equivalent forms.

Lesson 2 • Norton Equivalent Concept

Introduces the Norton model as a parallel current source and resistance at two terminals. Connects the concept to Thevenin duality for unified understanding.

Lesson 3 • Thevenin–Norton Conversion

Demonstrates direct algebraic conversion between Thevenin and Norton equivalents. Enables flexible switching between forms to simplify cascaded network analysis.

Lesson 4 • Norton Analysis with Dependent Sources

Extends Norton derivation to circuits containing dependent sources using test-source methods. Mirrors the Thevenin dependent-source approach for consistent technique.

Lesson 1 • Deriving the Maximum Power Condition

Uses calculus-based optimisation to derive RL equals Rth as the maximum power condition. Provides rigorous proof and graphical confirmation.

Lesson 2 • Power Transfer Fundamentals

Reviews power delivered to a load as a function of load resistance using Thevenin equivalents. Sets up the optimisation problem central to the theorem.

Lesson 3 • Maximum Power Calculation

Computes the maximum power value and the corresponding load current and voltage. Connects the result directly to Thevenin parameters for quick calculation.

Lesson 4 • Practical Applications and Limitations

Examines real-world scenarios where maximum power transfer is and is not the design goal. Distinguishes power maximisation from efficiency maximisation in engineering practice.

Lesson 1 • Applying the Reciprocity Theorem

Uses reciprocity to swap source and measurement locations without changing the response ratio. Reduces analysis effort in symmetric and ladder network problems.

Lesson 2 • Reciprocity Theorem Statement and Proof

States the reciprocity theorem and proves it for linear bilateral networks using matrix methods. Establishes the symmetry property of the network response.

Lesson 3 • Millman's Theorem Derivation

Derives the Millman equivalent voltage for multiple parallel branches with series sources. Shows the theorem as a direct consequence of node-voltage analysis.

Lesson 4 • Applying Millman's Theorem

Demonstrates step-by-step application of Millman's theorem to multi-branch circuits. Highlights efficiency gains over full node-voltage analysis.

Lesson 1 • Multi-Theorem Problem Solving

Solves complex circuits by sequentially applying two or more theorems in a coordinated strategy. Builds fluency in transitioning between theorem frameworks mid-analysis.

Lesson 2 • Theorem Selection Strategy

Develops a decision framework for choosing the most efficient theorem given circuit topology and analysis goal. Prevents trial-and-error approaches in complex problems.

Lesson 3 • Capstone Circuit Analysis Problems

Presents industry-representative circuit problems requiring full theorem integration and verification. Consolidates all course competencies into professional-level problem-solving practice.

Lesson 4 • Verification and Error Checking

Introduces systematic verification methods including power balance, KVL, and KCL checks. Ensures solution accuracy and builds professional analysis discipline.