Lesson 11

Norton’s Theorem Overview

  • Norton’s Theorem is the inverse of Thevenin’s Theorem, both based on the principle of duality.

  • Important dualities include:

    • Series circuits correspond to parallel circuits.

    • Short circuits correspond to open circuits.

    • Current is constant in series circuits; voltage is constant in parallel circuits.

Application and Importance

  • Complex circuits can be transformed into equivalent parallel circuits with a current source replacing the original voltage source.

  • The method requires understanding the Current Divider’s Principle (CDP).

  • Norton’s and Thevenin’s Theorems are linked by the equivalent resistance of the circuit, termed 'looking-backward-resistance'.

  • Norton’s Theorem is applicable in determining the correct size of circuit current protection, essential in electrical system designs to prevent faults.

Comparison with Thevenin’s Theorem

  • Norton’s Theorem operates based on the short-circuit current whereas Thevenin’s relies on the open-circuited terminal.

  • Both methods are useful in multi-source networks; Norton is particularly effective for fault analysis.

  • A comparison of methods shows:

    • Kirchhoff's Law: Equation sets relate to branches.

    • Maxwell’s Equations: Equation sets relate to meshes.

    • Nodal Analysis: Equation sets relate to nodes.

    • SPT (Source Preservation Techniques): Number of voltage sources correlated with Ohm's Law.

    • Thevenin’s Theorem: Involves calculation of equivalent resistance (RTH), voltage (VTH), and net equivalent circuit (TEC).

Steps Under Norton’s Theorem

  1. Determine the Norton equivalent resistance (RN, same as RTH).

  2. Calculate the short-circuit current (IN).

  3. Construct the Norton Equivalent Circuit (NEC).

Power Calculation Example

  • Calculate power consumed by R3 with 30Ω resistance using Norton’s Theorem:

    • Establish short-circuit condition for R3 to find IN.

    • Using given data, apply Maxwell’s Equations to compute IN.

    • Create the Norton Equivalent Circuit (NEC) with IN = 7 A and resistance RN.

    • Utilize Current Dividers Principle for resistance (30Ω) to find the distribution of current.

    • Solve for power:

      • P = (IN)² × R3 = (1.27)² × 30Ω = 48.39W.

Comparison of Theorems

Norton’s Theorem

Thevenin’s Theorem

RN

RTH

IN

VTH

Current source

Voltage source

Equivalent circuit

Equivalent circuit

Parallel circuit

Series circuit

Key Terms

  1. Short circuit current

  2. Transient current

  3. Fault current

  4. Current protection

  5. Circuit breakers

  6. Advantages of Norton’s Theorem over Thevenin’s Theorem

  7. Disadvantages of Norton’s Theorem

Acknowledgements

  • Thank you to Engr. Arturo Tadeos, Rizal Technological University, for the insights on Norton’s Theorem.