58-northons-theorem

Norton’s theorem states that any collection of voltage sources, current sources, and resistors is electrically equivalent to an ideal current source with a single equivalent resistor.

Steps of the analysis:

  1. Find equivalent resistor of the circuit by replacing load resistor with an open circuit and in the rest of the circuit replace voltage sources with short connection and current sources with open circuit and calculate equivalent resistance.
  2. Find equivalent current by finding equivalent voltage across open circuit first.
  3. Divide equivalent voltage across open circuit with equivalent resistor calculated in step one.
  4. Return load resistance back to initial electric circuit and replace rest of the circuit with Norton equivalent.

Norton reduces analysis electric circuit down to a single resistance in parallel with a constant current source.

In the following example, current I5 is calculated by replacing rest of the circuit with Norton equivalent.

norton

First step is to find equivalent resistance of the rest of the circuit:

norton01

Norton equivalent resistance for given circuit is
RN=(R1+R2)||R3 i.e.

norton_eq_01

Next step is to find voltage across points A and B:

norton02

Voltage across A and B can be simply found by using superposition theorem.

norton_eq_02

Third step is to find Norton current by dividing VAB with RN.

norton_eq_03

Forth step is to replace circuit with Norton equivalent.

norton04

Current I5 can be easily calculated as simple current divider.

norton_eq_04

With Norton equivalent, number of equations is significantly reduced, comparing with direct application of Kirchhoff circuit laws that would require two equations according KCL and three according KVL.

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