(5) UNIT-1I DC Circuits I One Shot I Electrical Engg. I by Avinash Sir I Gateway Classes I AKTU

Overview of DC Circuits (Unit 1)

• Focus on two major analysis methods: Mesh Analysis and Nodal Analysis.

• Emphasis on numerical problems stemming from these two methods.

• Definitions and basic concepts will also be part of the syllabus.

• History of questions indicates a pattern: main topics yield significant marks while smaller topics usually generate short questions.

Syllabus Details

Key Concepts

• Electric Circuit Elements: Active and Passive Elements, Voltage and Current Sources.

• Types of Sources: Understanding linear, unilateral, and bilateral elements.

• Kirchhoff's Laws: Kirchhoff Current Law (KCL) and Kirchhoff Voltage Law (KVL).

• Numerical Focus: Both Mesh Analysis and Nodal Analysis will be heavily weighted, potentially yielding 7 marks.

Active and Passive Elements

• Active Elements: Provide energy to the circuit (e.g., voltage sources, current sources, batteries).

• Passive Elements: Consume energy (e.g., resistors, capacitors).

• Energy transfer: Active elements supply energy which passive elements consume.

Unilateral and Bilateral Elements

• Bilateral Elements: Characteristics that do not change irrespective of current direction (e.g., resistors).

• Unilateral Elements: Characteristics change based on current direction (e.g., diodes).

Linearity and Non-linearity

• Linear Elements: Follow Ohm's Law, maintaining a constant ratio of voltage to current (e.g., resistors, inductors).

• Non-Linear Elements: Do not maintain a constant ratio (e.g., diodes exhibit varying characteristics based on voltage).

Kirchhoff's Laws

Kirchhoff Current Law (KCL)

• The total current entering a junction is equal to the total current leaving the junction.

• Mathematically: [I_{in} = I_{out}]

• Alternatively, the algebraic sum of all currents at a node is zero.

Kirchhoff Voltage Law (KVL)

• In any closed loop, the sum of all voltages and potential differences must equal zero.

• Mathematically: [ΣV = 0]

Mesh Analysis

Procedure for Mesh Analysis

1. Identify individual loops (meshes) in the circuit.

2. Assign mesh currents for each independent mesh.

3. Apply KVL to each mesh to formulate equations.

4. Solve the resulting equations simultaneously to find mesh currents.

   • Check examples where questions deal with current sources common between meshes.

   • Use Super Mesh concept when current sources introduce dependency between loops.

Nodal Analysis

Procedure for Nodal Analysis

1. Identify the nodes in the circuit.

2. Choose a reference node (usually ground).

3. Assign voltages to the other nodes relative to the reference node.

4. Apply KCL at each node to set up equations based on incoming and outgoing currents.

   • Typically results in equations that can be solved for node voltages.

Practice Problems

• Emphasis on solving previous exam questions for better preparation.

• Numerical problems will heavily relate to defined methods (Mesh and Nodal Analysis) discussed.

• Understanding the process and methodology is crucial to solving the problems accurately.