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Steps to find Norton resistance

Short answer

Remove the load, short-circuit independent voltage sources, open-circuit independent current sources, then find the equivalent resistance between the terminals. Example: for a 20 V source with 4 Ω and 6 Ω, RN = 4 Ω ∥ 6 Ω = 2.4 Ω.

Write down the steps to calculate Norton's equivalent resistance in the circuit with a suitable example.

Norton's equivalent resistance (R_N) is the resistance seen from the two terminals of the network with all independent sources deactivated. It is found as follows.

Steps

  1. Identify the two terminals (a, b) across which the Norton equivalent is required, and remove the load.
  2. Replace every independent voltage source by a short circuit.
  3. Replace every independent current source by an open circuit. (Dependent sources stay.)
  4. Reduce the remaining resistors between a and b by series, parallel (or star-delta) rules. This single resistance is R_N (equal to R_th).
  5. Connect R_N in parallel with the Norton current source I_N (the short-circuit current between a and b).
 Step 2-3 (sources off)          Result
 o--+----[R1]----+--o a          o---+-------o a
    |            |                  [R_N]
   [R2]         [R3]                  |
    |            |                o---+-------o b
 o--+------------+--o b

Example

A 20 V source with R₁ = 4 Ω in series, R₂ = 6 Ω across the output terminals a-b.

  • Turn the 20 V source off (short): R₁ = 4 Ω is now in parallel with R₂ = 6 Ω between a and b.
  • R_N = 4 ∥ 6 = 4 × 6/10 = 2.4 Ω

For the full Norton equivalent: short a-b, I_N = 20/4 = 5 A. So the equivalent is a 5 A source in parallel with 2.4 Ω. Open-circuit voltage = 5 × 2.4 = 12 V (check: 20 × 6/10 = 12 V).

✓ Answer checked by Claude Opus 5.5 (high effort)

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