What is Superposition theorem: Definition and 26 Discussions

The superposition theorem is a derived result of the superposition principle suited to the network analysis of electrical circuits. The superposition theorem states that for a linear system (notably including the subcategory of time-invariant linear systems) the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internal impedances.
To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by:

Replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential i.e. V=0; internal impedance of ideal voltage source is zero (short circuit)).
Replacing all other independent current sources with an open circuit (thereby eliminating current i.e. I=0; internal impedance of ideal current source is infinite (open circuit)).This procedure is followed for each source in turn, then the resultant responses are added to determine the true operation of the circuit. The resultant circuit operation is the superposition of the various voltage and current sources.
The superposition theorem is very important in circuit analysis. It is used in converting any circuit into its Norton equivalent or Thevenin equivalent.
The theorem is applicable to linear networks (time varying or time invariant) consisting of independent sources, linear dependent sources, linear passive elements (resistors, inductors, capacitors) and linear transformers.
Superposition works for voltage and current but not power. In other words, the sum of the powers of each source with the other sources turned off is not the real consumed power. To calculate power we first use superposition to find both current and voltage of each linear element and then calculate the sum of the multiplied voltages and currents.
However, if the linear network is operating in steady-state and each external independent source has a different frequency, then superposition can be applied to compute the average power or active power. If at least two independent sources have the same frequency (for example in power systems, where many generators operate at 50 Hz or 60 Hz), then superposition can't be used to determine average power.

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  1. L

    Engineering Solve Superposition Theorem for R1, R2 Circuit

    i have this question and i just want to make sure i am on the right track as i know there are quite a few steps to this to get to the final soultions i need to find Current at r1 voltage at r1 current at r2 voltage at r2 i have so far split this into 2 drawings so i am dealing with one power...
  2. J

    I What is so compelling in the superposition theorem?

    My question is, if the determinism theorem is a good explanation, which covers all holes of the entanglement experiment. why are people still concluding its a 'spooky' superposition which is only determined by a measure and then somehow affects the other measurement. What am I missing? Why is...
  3. A

    Engineering Is my method of solving this correct? Superposition theorem

    Hello! Consider this circuit Now I want to calculate the current Ik. The values are given as follows; Uq1 = 12 V Uq2 = 18V R1 = R2 = 8 Ohm R3 = R4 = 20 Ohm My approach was using the Superposition theorem. First I deactived Uq2 and left Uq1 active. Now if I am not mistaken the resistors R2 R3...
  4. S

    Engineering Please help me with this circuit question using the superposition theorem

    I have tried many times to solve this network, but can't understand how to get current in each resistors by superposition theorem. Please help me to solve and find currents in each 3 resistors with solution. Note:- The figure is attached below.
  5. P

    Superposition Theorem with complex numbers

    1. Homework Statement . Figure 1 shows a 50 Ω load being fed from two voltage sources via their associated reactances. Determine the current i flowing in the load by: (a) Thevenin's theorem (b) Superposition (c) Transforming the two voltage sources and their associated reactances into current...
  6. D

    Applying the superposition theorem

    I am wondering is someone could comment on a question I have recently answered. I have attached the question and my answer. Apologies for not following the standard procedure of Latex but there are drawings associated with this question. I answered section A and my results are written on the...
  7. G

    Engineering AC circuit with a switch -- analysis

    Homework Statement Given the circuit of sinusoidal current (attachment1) with given data: \underline{Z_3}=200(3-j4)\Omega,\underline{Z_4}=100(3+j20)\Omega,\underline{Z_5}=100(3+j4)\Omega,\underline{Z}=100(2+j5)\Omega,\underline{I_{g2}}=-10(2-j)mA. After the switch is closed, the increment of...
  8. N

    Superposition Theorem (basic query)

    This relates to a homework question which I have spent considerable time on and although I understand the concepts, the process of getting to the answer is difficult because of several different 'versions' of the right answer I see. The relevant threads are...
  9. I

    Linearity and superposition theorem

    Homework Statement For the network of constant current shown in Figure 4 it is known that R1 = 50 Ω and , R = 10 Ω. When the switch P is in the 1-position , current I = 50 mA and Ip = 70 mA known i . When the switch P is in the 2-position , current I' = 40 mA and Ip' = 90 mA are known ...
  10. E

    Solve Superposition Theorem Homework: 50Ω Load

    Homework Statement FIGURE 1 shows a 50 Ω load being fed from two voltage sources via their associated reactances. Determine the current i flowing in the load by: Superposition Theorem Homework Equations [/B]The Attempt at a Solution :[/B] see attached files as I can not write in itex and...
  11. B

    Proof of superposition theorem for linear circuits

    Can someone link me/explain to me the proof of this theorem? I can't seem to find it online. Thanks! BiP
  12. W

    The superposition theorem for electrical circuits

    Hi fellow physicist! I have some trouble with finding a valid argument, for why the superposition theorem should be fulfilled for electrical circuits - there only containing resistors, capacitors and inductors - where the sources of the emf. are connected in series. Thanks in advance.
  13. D

    The superposition theorem with dependent sources

    Homework Statement Use the superposition principle to determine the value of Ix. Homework Equations I1+I2+I3=0 KCL V1+V2+V3=0 KVL Ix'+Ix''= answer The Attempt at a Solution So I understand how to get Ix' its just standard KVL it is -10+2Ix'+Ix'+2Ix'=0 which solving for Ix' gives 2A...
  14. R

    Δ & Y and Superposition Theorem?

    Homework Statement A black box with three terminals, a, b and c, contains nothing but three resistors and connecting wire. Show that no external measurement can distinguish between these two possible set-ups, known as Delta and Y: http://i45.tinypic.com/mcd9gp.png Is there any other...
  15. P

    Finding the current through a resistor using superposition theorem.

    Homework Statement We have this circuit. The problem states to find i, or the current through the 3 ohm resistor. Homework Equations V = IRThe Attempt at a Solution I've started by shorting out both voltage sources and leaving only the current source in the circuit. I paralleled the 4ohm...
  16. C

    Wrong final result in superposition theorem

    I have this assignment, basically I had to do the same thing in simplified way and then superposition theorem. Apparently the answers don't match. I'm pretty sure the mistake is in superposition theorem. It could be some really stupid and simple mistake I made since I'm no good at this at all...
  17. W

    Voltage and current source in superposition theorem

    why we take current source as a open and voltage source as a short in superposition theorem. is this is because of its internal resistance or any other reason exist?
  18. R

    Superposition theorem problem.

    In the problem attached do you use superposition theorem. if so how do you use it? I don't know how to solve circuits with 2 voltages.
  19. M

    Superposition theorem problem

    Homework Statement Homework Equations Hi, I have the following superposition theorem problem to find the current in each branch of the network shown in the following figure: The Attempt at a Solution I have removed the voltage sources separately till now by short circuiting the other...
  20. J

    Current Sources in Superposition Theorem

    Why do we replace current sources with open circuits when using the Superposition Theorem while we replace batteries with wire?
  21. V

    Solve Vo Using Superposition Theorem for Circuit

    Homework Statement Use the superposition theorem to find Vo in the circuitHomework Equations The Attempt at a Solution i made 8A source 0 so the first equation using KVL becomes: 10i1 = -20 i1 = -2 then making the 20V source 0, the next KVL equation becomes: i think it's 5i2-8 = 0 i2 = 8/5 i...
  22. F

    Solving Superposition Theorem for I(R1)

    Homework Statement Hi all I have been struggling to find the right ans for the I(R1) in this circuit. First i consider only the voltage source by opening the current source. As such i find that I'(R1) = (4-0.7)/1K = 3.3mA Secondly i consider the current source by shorting the...
  23. K

    Engineering Superposition Theorem Circuit, need some help

    Just found this forum and found some great help here so far just reading some posts. But I am stuck on a question in my homework. I am asking you to help check my work and make sure I am going in the right direction. I missed my lecture due to illness and have to figure this out on my own. Thank...
  24. A

    Solving a Problem using Superposition Theorem

    Please solve this problem using Superpotion theorem Homework Statement ‐ Calculate the voltage, current & power through Resistor R9. ‐ Test & Simulation results by using superposition theorem by using ECADtool. Homework Equations The Attempt at a Solution
  25. J

    Solving Circuit with Superposition Theorem

    I was working on this circuit. http://img404.imageshack.us/img404/3537/imptm6.jpg The problem asks to find the current through the R2 branch... Heres my approach and questions... Start from the opposite end of the circuit...combine the 2 parallel resistors R2 and R3...the V2 goes to...
  26. S

    Calculating Current Using Superposition Theorem

    1. Using the superposition theorem, calculate the the current in the right-most branch in the following circuit. http://img329.imageshack.us/img329/1190/superpositionmp1.png Attempt at solution. I basically followed the theorem, Both voltage sources in the circuit have the same polarity...
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