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Norton’s Theorem simplifies complex linear circuits into a single current source and resistor for easier analysis. ​

STATEMENT OF NORTON’S THEOREM

  • Norton’s Theorem states that any linear circuit can be replaced by a constant current source in parallel with a resistor. ​

EXPLANATION

  • The document explains the application of Norton’s Theorem using resistors and voltage sources. ​
  • It describes the process of calculating the Norton equivalent current and resistance. ​

STEPS FOR SOLVING NORTON THEOREM

  • Step 1: Short circuit the load resistance. ​
  • Step 2: Calculate the short-circuit current using mesh or nodal analysis. ​
  • Step 3: Short circuit voltage sources and open circuit current sources. ​
  • Step 4: Determine the Norton equivalent resistance. ​
  • Step 5: Draw the equivalent circuit.
  • Step 6: Calculate the load current using the formula. ​

EXAMPLE 1

  • The example demonstrates finding the Norton equivalent circuit with given resistors and voltage sources. ​
  • The short-circuit current (I_N) is calculated as 3.75 A.
  • The Norton equivalent resistance (R_N) is found to be 2 Ω. ​

EXAMPLE 2

  • This example calculates the load current (I_L) across a 40 Ω resistor. ​
  • The short-circuit current is determined to be 2 A. ​
  • The Norton equivalent resistance is calculated as 6.67 Ω, leading to a load current of 0.286 A. ​

EXAMPLE 3

  • The example finds the current through a 1 Ω resistor using Norton’s theorem. ​
  • The short-circuit current (I_N) is calculated as 0.64 A.
  • The Norton equivalent resistance is determined to be 1.555 Ω, resulting in a load current of 0.389 A.

ADVANTAGES OF NORTON’S THEOREM ​

  • Norton’s theorem simplifies circuit analysis for load current, voltage, and power calculations. ​
  • It aids in determining the optimal load resistance for maximum power transfer. ​

Norton’s Theorem – Lesson 4

Engineering Institute of Technology