What is Superposition principle: Definition and 40 Discussions

The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input A produces response X and input B produces response Y then input (A + B) produces response (X + Y).
A function


{\displaystyle F(x)}
that satisfies the superposition principle is called a linear function. Superposition can be defined by two simpler properties; additivity and homogeneity














{\displaystyle F(x_{1}+x_{2})=F(x_{1})+F(x_{2})\,}


{\displaystyle F(ax)=aF(x)\,}
Homogeneityfor scalar a.This principle has many applications in physics and engineering because many physical systems can be modeled as linear systems. For example, a beam can be modeled as a linear system where the input stimulus is the load on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathematically; there is a large body of mathematical techniques, frequency domain linear transform methods such as Fourier and Laplace transforms, and linear operator theory, that are applicable. Because physical systems are generally only approximately linear, the superposition principle is only an approximation of the true physical behavior.
The superposition principle applies to any linear system, including algebraic equations, linear differential equations, and systems of equations of those forms. The stimuli and responses could be numbers, functions, vectors, vector fields, time-varying signals, or any other object that satisfies certain axioms. Note that when vectors or vector fields are involved, a superposition is interpreted as a vector sum. If the superposition holds, then it automatically also holds for all linear operations applied on these functions (due to definition), such as gradients, differentials or integrals (if they exist).

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  1. C

    Understanding the Superposition Principle in Circuit Analysis

    When, if ever, is it necessary to use the superposition principle in order to solve a circuit? Can any circuit with multiple independent voltage sources be solved without superposition?
  2. T

    Superposition Principle for two Voltage Sources (confusions about....)

    I have a question about natural limitations when the superposition principle for circuits is applicable. Possibly there is a quite elementary reason why the problem I'm going to present next fails, but up to now I haven't a precise reason why that's exactly the case. Could somebody help...
  3. F

    The orgin of the superposition principle of electric field

    Isn't the superposition principle of electric field just force being addable? Jackson's electrodynamics says it's based on the premise of linear Maxwell's equations. Which support(s) the superposition principle?
  4. D

    Find the electric field inside and outside of a spherical shell superposition

    Hi! I need help with this problem. I tried to solve it by saying that it would be the same as the field of a the spherical shell alone plus the field of a point charge -q at A or B. For the field of the spherical shell I got ##E_1=\frac{q}{a\pi\epsilon_0 R^2}=\frac{\sigma}{\epsilon_0}## and for...
  5. Hawkingo

    I What is the failure of superposition in quantum mechanics?

    In a book it says that "we know of quantum phenomena in the electromagnetic field that represents a failure of superposition,seen from the viewpoint of the classical theory." I want to about what quantum phenomena is he talking about? This was from the page 11 of the book Electricity And...
  6. J

    What's the superposition principle for group action?

    A very simple question: if given a vector ##v(t_0)## and two group functions ##G(t)## and ##G'(t)##, here ##t## is the parameter of time, the two group functions act on ##v(t_0)## simultaneously, then we can get a vector field ##v(t)##, then how to get ##v(t)##?
  7. Bloopy

    MATLAB: Verification of Superposition Principle

    Homework Statement Verify Superposition Principle using Matlab, given a DC source of 100V, an AC source of 50V, 60Hz and three resistances, R1=10 ohms, R2=20 ohms and R3=15 ohms. I created the circuit below and ran the program. Result: Homework Equations None, just running the program...
  8. A

    I Principle of superposition of states

    Upon reading Landau QM, the Principle of superposition of states, I got confused. It states (and i quote): "Suppose that, in a state with wave function Ψ1(q), some measurement leads with certainty to a definite result 1, while in a state with Ψ2(q) it leads to a different result 2. Then it is...
  9. Karolus

    B Superposition principle: clarifications

    What is the "superposition principle"? I have a confusion about one of the fundamental concepts of quantum mechanics, the principle of superposition This sounds, more or less: a linear combination with arbitrary coefficients of different quantum states is a new quantum state If I have (for...
  10. A

    Struggling with Electric force.... The Superposition Principle

    When I'm solving a superposition principle problem i get stuck and so confused with the signs. For example this problem Consider three point charges at the corners of a triangle, as shown at right, where q1 = 6.00 × 10−9 C, q2 = −2.00 × 10−9 C, and q3 = 5.00 × 10−9 C. Find the magnitude and...
  11. Z

    Satisfying the wave equation with 2 different speeds

    Hello, I have a wave of the form y = Asin(x-vt) + Asin(x+2vt) which I substituted into the wave equation to find out if it satisfies it. It didn't because of the speed of the left traveling wave being equal to 2v. What I got was: A[-sin(x-vt)-sin(x-2vt)] = 1/v2 * A[-v2sin(x-vt) -...
  12. sergiokapone

    Knoll (knob/bump) on the plate of the capacitor

    Homework Statement The inner surface of one of the plates flat charged capacitor has a small hemispherical knoll. Away from it the electric field in the capacitor is equal to ## E_0 ##. Using the principle of superposition find the field at the top and at the base of the knoll. Homework...
  13. G

    Superposition Principle to Solve Circuit

    Homework Statement Homework Equations KVL: ΣV = 0 KCL: ΣI = 0 v = iR The Attempt at a Solution I started by removing the independent current source to leave an open circuit. Then I attempted nodal analysis at nodes v1, v2, and v3: KCL @ v1: (v1 - v2)/10 = v1/40 KCL @ v2: (v2 - v1)/10 -...
  14. T

    Superposition principle for potential?

    Homework Statement A solid, conducting sphere of radius "a" and charge -Q is concentric with a spherical conducting shell of inner radius "b" and outer radius "c". The net charge on the shell is +3Q. Take the zero of electric potential to be at some point at infinity. a.) Use Gauss's law to...
  15. V

    Superposition principle and information

    I have a question about, perhaps, GCSE level physics, if not below, which, for some reason, is not explained anywhere I've looked up. Or, at least, I didn't find any explanation. The picture above is supposed to explain the concept of superposition. It depicts a pair of one-dimensional waves...
  16. L

    Emergent Properties-When is the Superposition Principle Inadequate

    So I understand the Superposition principle doesn't apply to non-linear systems. I want students to understand (in high school physics...which I will be teaching in about a year) that the superposition principle essentially says things add. So I wanted to come up with some examples when this...
  17. T

    Superposition Principle (EE)

    Homework Statement I have to find voltage at point 2 using superposition method. So, I drew one circuit with no voltage source and another with no current source, and then tried to analyze each one separately. (On the picture starting from left, its 10 volts, then 10ohms, then at top 5...
  18. S

    Need help understanding Superposition Principle

    need help understanding "Superposition Principle"..! hello everyone.. if we have a function y=f(x) then in-order to prove linearity we try to justify according to superposition principle as : let x1 and x2 be two inputs then f(x1+x2)=f(x1)+f(x2) please correct me if i am wrong upto here...
  19. D

    We know that superposition principle is valid in Quantum Mechanics

    because Schrodinger equation is a linear differential equation. How do we show that Schrodinger equation is a linear differential equation?
  20. I

    Electrostatics and the superposition principle.

    what is the whole concept of the superposition principle?
  21. N

    Superposition principle? How to algebraically add up two equations?

    Superposition principle? How to algebraically add up two equations?? How do you add up (λ (√3)) / (4pi(ε naught)R) (√3/2 i hat - 1/2 j hat) + (λ (√3)) / (4pi(ε naught)R) (√3/2 i hat + 1/2 j hat)? the 1/2 j hat cancels out right? but what do i do with everything else?
  22. R

    Superposition principle explained

    I'm taking an introductoruy course on QM and qubits and my professor is frustrating me by using anthropromorphic terms to decribe superposition. He says, " the electron doesn't make up its mind to be in the ground or excited state until the measurement". Can someone give me a better explanation?
  23. Q

    Gauss' Law with Superposition Principle

    Homework Statement A very long cylinder of radius R has positive charge uniformly distributed over its volume. The amount of charge is λ Coulombs per meter of length of the cylinder. A spherical cavity of radius R' < R, centered on the axis of the cylinder, has been cut out of this cylinder...
  24. H

    Focusing EM wave and the Linear Superposition Principle

    Consider a lens of diameter d and a focal length f >> d. Let the cross-section area of the lens be S = N*λ^2. Let a plane wave be focused from S to an area S1=λ^2. Then, by the linear superposition principle the electric field intensity in the area S1 will be N times greater than it was in...
  25. S

    Superposition principle and continuity

    hello i have question : how the superposition principle proves continuity of ψ in potential barrier
  26. G

    Understanding the Limitations of Superposition Principle in Electronics

    According to superposition principle the circuit involved must be linear and bilateral right? But how comes the theorem is sometimes used in some of electronics problems example the diode circuits of which are unilateral circuits... Can anyone please explain me clearly the limitations of this...
  27. G

    Engineering Superposition principle applied to a linear circuit

    Homework Statement I have to find I3, I've already easily found the first component I3| but i don't understand how i can get I3||. I thought about a Wheatstone bridge but doesn't work looking at the data. The result is I3=-7 A
  28. B

    Showing Superposition Principle with Time-Dependent Schrödinger Equation

    Homework Statement Show that, if psi1 and psi2 are both solutions of the time-dependent Schr¨odinger equation, so is c(subscipt1) psi1 + c(subscript2) psi2 (where c1 and c2 are arbitrary constants). Homework Equations The Attempt at a Solution every source I've consulted so far...
  29. G

    Using the Superposition principle to solve a linear circuit

    I tried it many times but i don't understand how to start and which are the first steps. I started like this: Solve for V1: Vr1 = V1 * (R1/R1+(R2||(R3+R4))) = 5 V I'1 = Vr1/R1 = 1 A I'2 = I'1 * [(R1+R2)||(R3+R4)]/(R3+R4) = 0,6 A. is that right?
  30. N

    Can we apply superposition principle for states in Fock space?

    Please teach me this: In QTF theory book,I have not seen what saying about probability of creating or anihilating particle(quantum).So I wonder whether we can apply superposition principle for the states with different numbers of particles in Fock space. Thank you in advanced.
  31. H

    Superposition principle in arbitrary medium

    Does the superposition principle for wave equations (say electromagnetic) hold also for non homogeneous and anisotropic media? I.e. can one always represent a wave traveling in an arbitrary direction as a sum of waves propagating along the principal axes of, e.g. dielectric tensor \epsilon_{ik}...
  32. J

    Superposition principle and charges from infinity

    This is not a homework assignment but a question from a past exam paper as i am studying for an exam on monday. I am one of only 3 out of 150 who have never done physics before this, the first year of an electronics degree. I would really appreciate any help. 1) A charge q1=1e-4C is in a...
  33. A

    Linear superposition principle applied to electric potential

    If I'm going to apply the superposition principle and say something like V = V_1 + V_2, I need to make sure that my V_1 and V_2 are established with a common zero point for the potential, right? So, for example, one of them can't have been determined taking the zero point of the potential to be...
  34. S

    Magnitude of Electric field using superposition principle

    Homework Statement Two charges, +q and -q, are located in the x-y plane at points (0,+d/2) and (0,-d/2), respectively. Calculate the magnitude of the electric field at point P with the superposition principle. Data: q=37.0 nanoCoulombs, d=4.60mm and P at x=92.0mm. Homework Equations E...
  35. E

    Using the superposition principle

    Homework Statement Find I in the circuit using the superposition principle Homework Equations superposition: I = i_1 + i_2 + i_3 The Attempt at a Solution for i_1 we neglect the 12V and the 4A sources: (8 + 2 + 6)i_1 - 16 = 0 i_1 = 1A for i_2 we neglect the 16V and the 4A sources: (8 + 2 +...
  36. B

    Proving the superposition principle

    Homework Statement Hi everyone. I am trying to prove the superposition principle for linear homogeneous equations, which states that if u(t) and w(t) are solutions to y' + p(t)y = 0, then u(t) + w(t) and k(u(t)) are also solutions for any constant k. The Attempt at a Solution I...
  37. I

    Proof of Superposition Principle

    Hey, I was recently reading "If an electron can be in 2 places at once, why can't you?" in the new Discover magazine when I came across the superposition principle ( I have heard of it before, just never really looked into it). They said that evidence of the phenomena could be found in the...
  38. siddharth

    Superposition principle to find the force due to a system of charges

    To find the force due to a system of charges, we can find the force on a charge due to the other charges and add the vectors. In this context, my school textbook says, "Superposition principle should not be regarded as obvious, or equated with the law of addition of vectors. It says two...
  39. E

    Superposition Principle Question

    So if we have a particle in a one dimensional box with walls at x=0 and x=a. Now suppose one of the walls is moved in a time short compared to the natural period 2pi/w1, where (h/2pi)w1=E. If the energy of the particle is measured soon after this expansion, what value of energy is most likely to...
  40. T

    Superposition principle and linearity

    hello folks! this is my first post on the forums and I kick off with an interesting question... I had been coming across the principle of superposition for quite some time and to admit frankly didn't ever understood it. The most abstruse aspect is to comprehend how can to different...