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Understanding Thevenin's and Norton's Theorem

Sep 6, 2024

Thevenin's and Norton's Theorem Lecture Notes

Introduction

  • Lecturer: Dhruvi
  • Topic: Thevenin's and Norton's Theorem

Thevenin's Theorem

  • Definition: Any two terminals of a network can be replaced by an equivalent voltage source (Vth) and an equivalent series resistance (Rth).

Key Components

  • Voltage Source (Vth): The voltage across the two terminals with the load removed.
  • Series Resistance (Rth): The resistance of the network measured between the two terminals with the load removed.

Steps to Determine Thevenin Equivalent

  1. Identify the terminals (A and B) of the network.
  2. Calculate Vth:
    • Remove any load resistor (if present).
    • Apply Kirchhoff's Voltage Law (KVL) to find the voltage across terminals A and B.
  3. Calculate Rth:
    • After finding Vth, replace the voltage source with a short circuit to find the current (I1).
    • Use the formula: Rth = Vth / I1.

Example Numerical Problem

  1. Given Circuit: Calculate the equivalent network for terminals A and B.
  2. KVL Application: For a single mesh:
    • Equation: 5 - 20 I1 = 0
    • Solution gives: I1 = 0.25 A.
  3. Calculate Vth:
    • Equation: 5 - 10 I1 + 8 I1 - Vth = 0
    • Result: Vth = 4.5 V.
  4. Calculate Rth:
    • Find I1 (2.25 A) using short circuit and then calculate Rth = Vth / I1 = 4.5 V / 2.25 A = 2 Ohms.
  5. Final Thevenin Equivalent:
    • Vth = 4.5 V with Rth = 2 Ohms.

Norton's Theorem

  • Definition: Any two terminals of a network can be replaced by an equivalent current source (In) and an equivalent parallel resistance (Rn).

Key Components

  • Current Source (In): The equivalent current flowing through the load.
  • Parallel Resistance (Rn): Resistance seen by the load.

Steps to Determine Norton Equivalent

  1. Identify terminals (A and B) of the network.
  2. Calculate Vth (same method as in Thevenin's) and use it to find In.
  3. For current equations, assign mesh currents and apply KVL.
  4. Calculate In and Rn using the formula: Rn = Vth / In.

Example Numerical Problem

  1. Given Circuit: Find Norton's equivalent network across A and B.
  2. KVL Application: Set up equations for multiple meshes to find I1 and I2.
  3. Calculate Vth: Use KVL on the outer loop to find Vth = 2.4 V.
  4. Calculate In: Solve mesh equations to find currents (both I1 and I2).
    • Result: In = 0.25 A.
  5. Calculate Rn: Rn = Vth / In = 2.4 V / 0.25 A = 9.6 Ohms.
  6. Final Norton Equivalent:
    • Current source In = 0.25 A parallel to Rn = 9.6 Ohms.

Conclusion

  • Thevenin and Norton theorems allow simplification of complex circuits.
  • Equivalent circuits can help analyze circuits more easily.
  • Encouragement to like, share, and subscribe for more content.

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