Understanding Thevenin's Theorem Basics

Sep 20, 2024

Thevenin's Theorem Presentation Notes

Introduction

  • Discussion on Thevenin's Theorem.
  • Named after Léon Charles Thévenin, a French engineer.
  • Developed in 1883.

Purpose of Thevenin's Theorem

  • Used when elements in a circuit are variable while others are fixed.
  • Prevents the need to analyze the entire circuit each time a variable element is changed.
  • Replaces the fixed part of the circuit with an equivalent circuit for simplification.

Thevenin Equivalent Circuit

  • The equivalent circuit consists of:
    • A voltage source (V_th) connected in series with a resistor (R_th).
  • Benefits of using the Thevenin equivalent circuit:
    • Simplifies calculations when variable components change.

Statement of Thevenin's Theorem

  • A linear bi-directional two-terminal network can be replaced by an equivalent network with:
    • Voltage source V_th (open circuit voltage).
    • Resistor R_th (input or equivalent resistance).

Finding V_th and R_th

  1. Calculation of V_th:

    • Remove the load resistor and open circuit the branch.
    • Use nodal analysis to determine the voltage at the principal node (V_x).
    • Apply Kirchhoff's Current Law (KCL):
      • i1 + i2 + i3 = 0.
    • Calculate currents:
      • i1 = (V_x - 32) / 4
      • i2 = V_x / 12
      • i3 = -2 (opposite direction).
    • Rearrange and solve to find:
      • V_th = 30 volts.

  2. Calculation of R_th:

    • Open circuit the load resistance and turn off all independent sources:
      • Replace independent sources with short/circuit as necessary.
    • Calculate equivalent resistance:
      • R_th = R_4 (parallel with) R_12 + 1.
      • Resulting in R_th = 4 ohms.

Thevenin Equivalent Circuit Summary

  • Thevenin equivalent circuit:
    • Voltage: V_th = 30 volts.
    • Resistance: R_th = 4 ohms.

Load Resistor Analysis

  • Calculate the current (I_L) through R_L for two cases:
    1. Case 1 (R_L = 6 ohms):
      • I_L = 30 / (4 + 6) = 3 amperes.
    2. Case 2 (R_L = 16 ohms):
      • I_L = 30 / (4 + 16) = 1.5 amperes.

Conclusion

  • Thevenin's Theorem allows for simplified calculations in complex circuits with variable elements.
  • Further exercises on Thevenin's Theorem will be covered in future lectures.