Norton Theorem

Norton theorem is an analytical method used to convert a complex circuit into a simple equivalent circuit consisting of a single resistance parallel to a current source.

Norton Theoremsays, "Any linear circuit containing several energy sources and resistance can be replaced with a single Constant Current generator in parallel with Single Resistance."

Regarding load resistance, R L is related to this single resistance, R S, all current sources are the value of resistance facing back to the grid with open circuit, and I S is the short circuit current in the output terminals as shown below. .

Norton Theorem
Norton Equivalent Circuit

The value of this "constant current" is the value that will flow when the two output terminals short circuit together, if the welding resistance is measured by looking back at the terminals (the same as Thevenin).

For example, consider our familiar circuit now from the previous section.

Norton Theorem

To find the Norton equivalent of the above circuit, we must first remove the center 40Ω load resistance and short-circuit terminals A and B to give us the following circuit .

Norton Theorem

When terminals A and B short circuit each other, the two resistors are connected in parallel with the two related voltage sources, and the currents flowing from each resistance, as well as the total short circuit current, can now be calculated as follows:

EU Short Circuit

Norton Theorem

If we short-circuit the two voltage sources and the open circuit terminals A and B, the two resistors are now effectively connected to each other in parallel.The value of the internal resistance Rs is found by calculating the total resistance in terminals A and B, which gives us the following circuit.

Norton Theorem

Find Equivalent Resistance (Rs)

Norton Theorem

After finding both short circuit current, Is and equivalent internal resistance, Rs, this gives us the norton equivalent circuit below.

Norton Theorem
Norton Equivalent Circuit

Ok, so far it is good, but now we need to solve it with the original 40Ω load resistance that connects to terminals A and B, as shown below .

Norton Theorem

Again, the two resistors are connected in parallel along terminals A and B, which give us total resistance:

Norton Theorem

When the load resistance is connected, the voltage between terminals A and B is given as follows:

Norton Theorem

Then the current flowing at 40Ω load resistance can be found as follows:

Norton Theorem

Once again, using norton theorem, the value of the current for I 3 is still calculated as 0.286 amps , which we found in previous lessons using Kirchhoff's circuit law.

Norton Theorem Summary

The basic procedure for solving a circuit using norton theorem is as follows:

  • 1.Remove load resistance R Lor the corresponding component.
  • 2.Find the R Sby short-circuiting all voltage sources or by open-circuiting all current sources.
  • 3.Find the IS by making a short circuit connection in the A-B output terminals.
  • 4. Find the current that passes through the R L load resistance.

In a circuit, the power supplied to the load is at maximum when the load resistance is equal to the weld resistance.In the next lesson, we'll look at the Maximum Power Transfer.The application of the maximum power trafer theorem can be applied to simple and complex linear circuits with variable load and is used to find load resistance, which leads to maximum power transfer to the load.