Breaking News
Home » Analyzing Electric Circuits » Norton’s Theorem. Easy Step by Step Procedure with Example (Pictorial Views)

Norton’s Theorem. Easy Step by Step Procedure with Example (Pictorial Views)

Norton’s Theorem

Easy Step by Step Procedure with Example (Pictorial Views)

This is another useful theorem to analyze electric circuits like Thevenin’s Theorem, which reduces linear, active circuits and complex networks into a simple equivalent circuit. The main difference between Thevenin’s theorem and Norton’s theorem is that, Thevenin’s theorem provides an equivalent voltage source and an equivalent series resistance, while Norton’s theorem provides an equivalent Current source and an equivalent parallel resistance.
Norton’s Theorem may be stated under:
Any Linear Electric Network or complex circuit with Current and Voltage sources can be replaced by an equivalent circuit containing of a single independent Current Source IN and a Parallel Resistance RN.
Simple Steps to Analyze Electric Circuit through Norton’s Theorem
  1. Short the load resistor
  2. Calculate / measure the Short Circuit Current. This is the Norton Current (IN)
  3. Open Current Sources, Short Voltage Sources and Open Load Resistor.
  4. Calculate /measure the Open Circuit Resistance. This is the Norton Resistance (RN)
  5. Now, Redraw the circuit with measured short circuit Current (IN) in Step (2) as current Source and measured open circuit resistance (RN) in step (4) as a parallel resistance and connect the load resistor which we had removed in Step (3). This is the Equivalent Norton Circuit of that Linear Electric Network or Complex circuit which had to be simplified and analyzed. You have done.
  6. Now find the Load current flowing through and Load Voltage across Load Resistor by using the Current divider rule. IL = IN / (RN / (RN+ RL)) ((For better understanding…check the solved example)
Example:

Find RN, IN, the current flowing through and Load Voltage across the load resistor in fig (1) by using Norton’s Theorem.

Click image to enlarge 

Norton's Theorem. Easy Step by Step Procedure with Examples and solved problems
Norton’s Theorem: Step by Step Procedure with Examples


Solution:-
Step 1.
Short the 1.5Ω load resistor as shown in (Fig 2).
Click image to enlargeNorton’s theorem  
Step 2.
Calculate / measure the Short Circuit Current. This is the Norton Current (IN).
We have shorted the AB terminals to determine the Norton current, IN. The 6Ω and 3Ω are then in parallel and this parallel combination of 6Ω and 3Ω are then in series with 2Ω.
So the Total Resistance of the circuit to the Source is:-
2Ω + (6Ω || 3Ω) ….. (|| = in parallel with).
RT = 2Ω + [(3Ω x 6Ω) / (3Ω + 6Ω)] → IT= 2Ω + 2Ω = 4Ω.
RT = 4Ω
IT = V / RT
IT = 12V / 4Ω
IT = 3A..
Now we have to find ISC = IN… Apply CDR… (Current Divider Rule)…
ISC = IN = 3A x [(6Ω / (3Ω + 6Ω)] = 2A.

ISC= IN = 2A.

Click image to enlargenorton equivalent circuit examples 
Step 3.
Open Current Sources, Short Voltage Sources and Open Load Resistor. Fig (4)
Click image to enlargenorton equivalent circuit examples 
Step 4.
Calculate /measure the Open Circuit Resistance. This is the Norton Resistance (RN)
We have Reduced the 12V DC source to zero is equivalent to replace it with a short in step (3), as shown in figure (4)  We can see that 3Ω resistor is in series with a parallel combination of 6Ω resistor and  2Ω resistor. i.e.:
3Ω + (6Ω || 2Ω) ….. (|| = in parallel with)
RN = 3Ω + [(6Ω x 2Ω) / (6Ω + 2Ω)]
RN = 3Ω + 1.5Ω
RN = 4.5Ω
Click image to enlargeNorton Theorem
Step 5.
Connect the RN in Parallel with Current Source INand re-connect the load resistor. This is shown in fig (6) i.e. Norton Equivalent circuit with load resistor.
Click image to enlarge

Norton Equivalent circuit
Norton Equivalent circuit

 

Step 6.
Now apply the last step i.e. calculate the load current through and Load voltage across load resistor by Ohm’s Law as shown in fig 7.
Load Current through Load Resistor…
IL = IN x [RN / (RN+ RL)]
= 2A x (4.5Ω /4.5Ω +1.5Ω) → = 1.5A
IL = 1. 5A
And
Load Voltage across Load Resistor…
VL = IL x RL
VL = 1.5A x 1.5Ω

VL= 2.25V

Click image to enlarge 

Finding the Load Current and Load Voltage through Norton's Theorem
Finding the Load Current and Load Voltage through Norton’s Theorem
Now compare this simple circuit with the original circuit of figure 1. Can you see how much easier it will be to measure/calculate the load current and Load Voltage for different load resistors through Norton’s Theorem? Only and only yes…

EasyEDA: A Powerful Free Circuit, Simulation & PCB Design Tool
Register now to use it for free in Your Browser. No Need to download. Lots of resources and Step by step tutorials

About Electrical Technology

All about Electrical & Electronics Engineering & Technology. Follow , Facebook , Twitter , Instagram , Pinterest & Linkedin to get the latest updates or subscribe Here to get latest Engineering Articles in your mailbox. Also, Follow

Check Also

DC Drives – Construction, Working & Classification of Electrical DC Drives

DC Drives – Construction, Working & Classification of Electrical DC Drives

What are DC Drives? Working & Operation of DC Drives DC drive technology is efficient, …

14 comments

  1. sir plz give me a name of books about circuit and analysis of network for clearing concepts.<br />

  2. Great article! Norton&#39;s Theorem can certainly be confusing for a beginner.

  3. great and thanku<br />

  4. Nortons theorem

  5. DINABANDHU PARAI

    I want to know the best refarance book which can give me the best concept about nortons / Thevein , super position theorem
    If u can pls help me
    Thank you

  6. Pls,why did they use (3/(3 6)) to solve for the nortons cuRrent

  7. fatima jawadu

    May you please help with the best book I can use for electrical engineering technology

  8. Thanks dude…..i hve exam in 3 hrs……ur post’s helped me a lot!!!

  9. Thanks sir a lot of thanks

  10. jomari Honrado

    why the CDR are not (RT / RX+RT) X IT make me confuse ?

  11. What if u r to find the current across the 6(ohm) resister?

Leave a Reply

Your email address will not be published. Required fields are marked *