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Find the value of Norton resistance at the terminals a-b for the circuit shown here. (where V = 10 V, I = 5 A, R1 = 9 Ω, R2 = 18 Ω, R3 = 4 Ω)

Find the value of Norton resistance at the terminals a-b for the circuit shown here. (where V = 10 V, I = 5 A, R1 = 9 Ω, R2 = 18 Ω, R3 = 4 Ω) Correct Answer <span style=" line-height: 107%; ">10 Ω</span>

Concept:

  • Norton’s Theorem states that “Any linear circuit containing several energy sources and resistances can be replaced by a single constant current source in parallel with a single resistor “.
  • It is an analytical method used to change a complex circuit into a simple equivalent circuit consisting of a single resistance in parallel with a current source.

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Steps to follow for Norton’s Theorem:

  • Calculate Norton’s current source by removing the load resistor from the original circuit and replacing it with a short circuit.
  • Calculating the current through a shorted wire.
  • Calculating the Norton resistance by removing all power sources in the original circuit (voltage sources shorted and current sources open).
  • Calculating total resistance between the open connection points.
  • Draw the Norton equivalent circuit, with the Norton current source in parallel with the Norton resistance.
  • The load resistor re-attaches between the two open points of the equivalent circuit.


Calculation:

After removing the independent sources, the circuit becomes as shown below.

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The equivalent resistance is,

RN = (9 || 18) + 4 = 10 Ω

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