What is Norton equivalent: Definition and 32 Discussions

In direct-current circuit theory, Norton's theorem (aka Mayer–Norton theorem) is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of terminals of the network, it can be replaced by a current source and a single resistor in parallel.
For alternating current (AC) systems the theorem can be applied to reactive impedances as well as resistances.
The Norton equivalent circuit is used to represent any network of linear sources and impedances at a given frequency.
Norton's theorem and its dual, Thévenin's theorem, are widely used for circuit analysis simplification and to study circuit's initial-condition and steady-state response.
Norton's theorem was independently derived in 1926 by Siemens & Halske researcher Hans Ferdinand Mayer (1895–1980) and Bell Labs engineer Edward Lawry Norton (1898–1983).To find the equivalent, the Norton current Ino is calculated as the current flowing at the terminals into a short circuit (zero resistance between A and B). This is Ino. The Norton resistance Rno is found by calculating the output voltage produced with no resistance connected at the terminals; equivalently, this is the resistance between the terminals with all (independent) voltage sources short-circuited and independent current sources open-circuited. This is equivalent to calculating the Thevenin resistance.

When there are dependent sources, the more general method must be used. The voltage at the terminals is calculated for an injection of a 1Amp test current at the terminals. This voltage divided by the 1 A current is the Norton impedance Rno. This method must be used if the circuit contains dependent sources, but it can be used in all cases even when there are no dependent sources.

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  1. G

    Thévenin and Norton circuits Exercise

    Figure: My attempt at a solution: a) ##\boxed{V_{TH}}## Current source equations ##\rightarrow \boxed{2=I_2-I_1}## Control variable equations ##\rightarrow V_1=4I_2\rightarrow \boxed{0=4I_2-V_1}## Super Mesh ##\rightarrow -0,5V_1+2I_1+I_2(4+8)-8I_3=0\rghtarrow...
  2. A

    Finding the Thevenin voltage

    Hello I'm trying to solve my homework assignment, I have successfully found the thevenin resistance which is equal to 3.75 but I'm stuck on how to even get started to find the voltage because there are too many components. I have shorted the load resistor which is called RL but there are too...
  3. cianfa72

    Formal proof of Thevenin theorem

    Hi, I am looking for a formal proof of Thevenin theorem. Actually the first point to clarify is why any linear network seen from a port is equivalent to a linear bipole. In other words look at the following picture: each of the two parts are networks of bipoles themselves. Why the part 1 -- as...
  4. B

    KCL got declined in Norton circuit of an ideal amplifier circuit

    Hi. Let's say we have a circuit like that, and we want to find the Thevenin/Norton circuit from a and b points. So for Vth, we calculate the Voc, in which we remove the 2K ohm resistor and calculate the Voc. I calculated it correctly. But I have problem in calculating the Norton current. So in...
  5. J

    When a short-circuit exists, how to find the current?

    I am not an English speaker, I apologize that I cannot use English well. I have a question calculating the IN. When the terminal a-b is short-circuited, is it right that the currents are zero at 2 ohm and 6 ohm resistances?(Because they are parallel with a short-circuit.) Also, because the...
  6. M

    Find the Norton equivalent resistance

    Homework Statement Find the Norton equivalent resistance Homework Equations Sum of resistance in a parallel circuit: 1/Rt = 1/R1 + 1/R2... Sum of resistance a series circuit: Rt= R1+R2... The Attempt at a Solution Don't know where to go from here:
  7. Y

    Why do I get different answers with different methods - Thevenin

    Homework Statement Determine the Thevenin equivalent of the following circuit: https://imgur.com/a/74UjA (Top image) Homework Equations - The Attempt at a Solution The last 3 images in the Imgur album are all different approaches. I can't figure out what the right one is, and why the other...
  8. Z

    How to know when to use Voc/Isc or Vtest/Itest for Thevenin?

    should you only apply the test sources when there are only independant sources in the circuit. Also would it be valid to zero all dependant source so that you are only left with independant sources and then apply the test source. It seems like i am always applying open and short circuit...
  9. kostoglotov

    Diode Question: need to understand why my approach is wrong

    Homework Statement A screenshot of the problem: imgur link: https://i.imgur.com/ljtoclm.png Homework EquationsThe Attempt at a Solution My first attempt at the solution was this: imgur link: https://i.imgur.com/TJcvOzy.jpg However, I have access to the worked solution, and it is...
  10. E

    Engineering Norton equivalent circuit?

    Homework Statement Is this simplified enough to be considered a norton circuit? Does the current source HAVE to be on the left? Homework Equations N/A The Attempt at a Solution N/A
  11. Aleksa Stanojlovic

    Norton Equivalent with dependet current source - Problem

    Hey everyone... I've tried to solve this problem with all kind of methods ,but I couldn't do it. I have tried to make an open circuit between R2 and R2 and then to find thevenin voltage and Ri but I have problem solving for thevenin voltage because of this dependent current source... Please give...
  12. Marcin H

    Find Norton Equiv. for Homework: V=IR

    Homework Statement Find the Norton equivalent at the terminals. Homework Equations V=IR The Attempt at a Solution I did the thevenin equivalent, but I'm not sure where to go from there. How do I get the Norton equivalent out of this? [/B]
  13. T

    Thevenin and Norton equivalent circuits

    Hi guys, Sorry if all you guys think this question is too easy. But I have a hard time to understand how to group the resistor. I suppose to find the the thevenin and Norton equivalent circuit. This is what i think about the combination of resistor. Req1= RL+1k Req2= Req1 ll 3.3k (3.3k after...
  14. T

    Thevenin and Norton Equivalent

    Homework Statement For this problem (pic attached) I did the open circuit calculations and found V1 (6v) and V2 (4v) and I know they are correct. However I am not sure if my Voc and Isc (open circuit voltage and short circuit current) calculations are correct. The Attempt at a Solution...
  15. A

    Engineering [Circuits] Calculating the Norton Equivalent

    Homework Statement Homework Equations The Attempt at a Solution I am trying to compute ##I_N##. I connected nodes a and b. The circuit after some simplification: $$\frac { 180-{ V }_{ 1 } }{ 20 } =\frac { 120-V_{ 1 } }{ 40 } \\ { V }_{ 1 }=240\quad V\\ \\ R=\frac { V...
  16. M

    Solving Norton Equivalent Circuits - Help Needed

    Homework Statement Having some Difficulty in starting the second question on this sheet. i have managed to find examples and worked my way through the first question, but unfortunately my tutor has decided to move onto pastures new, and we have an assignment to complete but no tutor which...
  17. X

    Thevenin and Norton Equivalent

    Homework Statement Find Vt and In Homework Equations KCL The Attempt at a Solution I found Rt to be 5.94 ohms (1/(1/7+1/9)+2) Then I am stuck. I know to find Vt (which is equal to Vopen circuit), I have to do a KCL in an open circuit, so my KCL equation is 2+Voc/3=Voc/4 So...
  18. T

    Engineering Norton Equivalent Circuit: Find i(sc) and R(t)

    Homework Statement The (b) circuit shown in the attached image is the Norton equivalent circuit of the (a) circuit. Find the value of the short-circuit current, isc, and Thévenin resistance, Rt. isc being the current that would flow through the two open nodes if they were shorted. The...
  19. P

    Engineering Norton Equivalent Circuit

    Homework Statement Question Homework Equations The Attempt at a Solution I tried using source transformation. I simplified the original circuit to the above circuit. I got Rnorton, however, I am a bit unsure on getting Isc. Is it possible to source transform the above circuit further? Or...
  20. C

    Norton Equivalent circuit

    Hi Can you please tell me how to find the Norton Equivalent or I should say the short circuit current in the attachment diagram? Norton resistance using two different methods but now question asks me to find resistance by dividing voltage of open circuit which I figure it out over current...
  21. T

    Norton Equivalent and Source Transformation problem

    Homework Statement Basically, I'm having trouble doing the source transformation and subsequently finding the norton equivalent for this circuit and I don't really know where to start. The circuit is attached where: i=3A V=90V Please help!
  22. P

    Engineering Thevenin and Norton Equivalent Circuits

    Homework Statement Consider this circuit. Find the Thévenin and Norton Equivalent Circuits (just need the 1st one). Homework Equations The Attempt at a Solution My attempt: Can someone check? Thanks a lot!
  23. R

    Engineering Use of superposition in Simple Circuits and Norton equivalent

    The problem statement 7. In the circuit below, the resistor R3 models a light bulb. a) Use superposition to find iX. b) Find the Norton equivalent as seen by the independent current source, iS2. c) Find the power delivered by the independent current source, iS2, in the circuit below. Diagram...
  24. M

    Bogged down on Norton equivalent problem

    Picture an 8ma ideal current source pointing downward in parallel to a 20kohm resistor on the left of this picture. Wouldn't these elements contribute to the voltage drop across A and B. Rth makes sense because the ideal voltage source will be shorted eliminating the last resistor but the...
  25. I

    Engineering Basic EE Norton Equivalent circuit

    Homework Statement Find norton equivalent circuit Homework Equations Rn=Rth The Attempt at a Solution Ok i got my R(n)=34 ohms because after you turn off independent sources the resistors are in series, then I short circuited a to be and I'm trying to use mesh analysis to solve...
  26. A

    Replace the emf+series resistance(s) by the Norton equivalent

    Homework Statement Write down the node-voltage matrix equation for the following circuit. Hence find the total power dissipated. (Hint: replace the emf+series resistance(s) by the Norton equivalents.) Homework Equations n/a The Attempt at a Solution The problem I'm having is that I...
  27. G

    Norton Equivalent Circuit

    Homework Statement Find the norton equivalent with respect to terminals a and b [PLAIN]http://img821.imageshack.us/img821/7177/nortonequivalent.jpg [Broken] Homework Equations KVL, KCLThe Attempt at a Solution I set i1 = .008 A Then I found the rest of the currents. KVL@ loop i2...
  28. James889

    Engineering Determining Norton Equivalent of a Circuit

    Hello, I have the following circuit: [PLAIN]http://img15.imageshack.us/img15/6981/nortonm.png [Broken] I need to determine the Norton equivalent for this circuit. I wonder whether the easiest way to solve this is by zeroing the independent source, connecting a test voltage source and...
  29. H

    Electric Circuit. Norton Equivalent current

    Electric Circuit. Norton/Thevelin Equivalents Unsolved Problem I used a node voltage equation to try and get Vth and the I in the short-circuit to get the Rth but it didn't work. Unsolved Problem I used a node voltage equation to get Vth and I in the short-circuit. Got Rth and...
  30. E

    Engineering Norton equivalent circuit

    I'm having trouble finding the norton equivalent resistance for the attached circuit. I reasoned that once you short the source, you just get the (3ohm+2ohm) in parallel with the 4ohm resistor. However the answer I'm getting is not the one given in the book (I get 2.22ohms, when it...
  31. R

    Norton Equivalent Circuit

    Homework Statement See picture: http://img88.imageshack.us/img88/8319/87671967.jpg [Broken] The answer is given as phasors I = 0.3536\angle45 Z = 2.828\angle-45 Homework Equations The Attempt at a Solution ZL = jwL = 2j Ohms ZC = -j/(wC) = -4j Ohms Can't do it by zeroing the sources as...
  32. S

    Thevenin and Norton Equivalent Circuits problem

    Hi, I found this question from a textbook: Suppose there are two black boxes, Box A has a 1V voltage source and 1ohm resistance (Thevein Circuit); and Box B has a 1A current source and 1ohm resistance (Norton Circuit). You only have access to the two terminals. How do you know which is which...
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