What is Phasor: Definition and 142 Discussions

In physics and engineering, a phasor (a portmanteau of phase vector), is a complex number representing a sinusoidal function whose amplitude (A), angular frequency (ω), and initial phase (θ) are time-invariant. It is related to a more general concept called analytic representation, which decomposes a sinusoid into the product of a complex constant and a factor depending on time and frequency. The complex constant, which depends on amplitude and phase, is known as a phasor, or complex amplitude, and (in older texts) sinor or even complexor.A common situation in electrical networks is the existence of multiple sinusoids all with the same frequency, but different amplitudes and phases. The only difference in their analytic representations is the complex amplitude (phasor). A linear combination of such functions can be factored into the product of a linear combination of phasors (known as phasor arithmetic) and the time/frequency dependent factor that they all have in common.
The origin of the term phasor rightfully suggests that a (diagrammatic) calculus somewhat similar to that possible for vectors is possible for phasors as well. An important additional feature of the phasor transform is that differentiation and integration of sinusoidal signals (having constant amplitude, period and phase) corresponds to simple algebraic operations on the phasors; the phasor transform thus allows the analysis (calculation) of the AC steady state of RLC circuits by solving simple algebraic equations (albeit with complex coefficients) in the phasor domain instead of solving differential equations (with real coefficients) in the time domain. The originator of the phasor transform was Charles Proteus Steinmetz working at General Electric in the late 19th century.Glossing over some mathematical details, the phasor transform can also be seen as a particular case of the Laplace transform, which additionally can be used to (simultaneously) derive the transient response of an RLC circuit. However, the Laplace transform is mathematically more difficult to apply and the effort may be unjustified if only steady state analysis is required.

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  1. L

    When Should Graphical Methods Be Used Over Nodal Analysis in Phasor Problems?

    1. I was just wondering WHEN i would use the graphical method to add phasors using cos law or sin law given inductors current lags voltage by 90 degrees and capacitors current leads by 90 degrees. When would i solve the problem graphically and when could I just use modified nodal analysis? when...
  2. C

    Finding voltage across elements in phasor diagram,

    Finding voltage across elements in phasor diagram, URGENT! Hi there, first time posting here, just caught up on a question with no worked solutions and it's driving me crazy! I've attached the question below,and the answer to b is v(t)= 5cos(2t-112). I can do part a but am struggling on...
  3. C

    Drawing a Balanced 3-Phase Resisitve-Capacitive Load Phasor Diagram

    Homework Statement From this diagram (see the attachment) I have to draw the phasor diagram showing the various voltages and current of balanced 3-phase resistive-capacitive load. Homework Equations I know from the capacitive current lead voltage by 90 degree The Attempt at a Solution...
  4. R

    Power Factor and Phasor Diagram

    OK, Hello! Have to make sure as I felt like I knew my stuff but failed my first exam, am I on the right tracks? Power Factor = Cosine of phase angle Phase angle = Tan Inverse ((XL-Xc)/R) (So you know) XL= Inductive Reactance Xc= Capacitive Reactance R = Resisstance Am I...
  5. C

    Convert Time Domain to Phasor Domain with Euler's Formula

    how is euler's formula useful? it must have something to do with converting from the time domain to the phasor domain and back, but i can do that without euler's formula
  6. V

    How Does Frequency Variation Affect Phasor Current in a Series Circuit?

    Impedance -- Current phasor In a series circuit of two elements, the voltage and current, for w = 2000 rad/s, are V = 150|-45° and I = 4,74|-116,6°.That variation in the frequency of the source would result in a phasor current of 6 amps? Assuming an unlimited variation in the frequency, what is...
  7. S

    About phasor voltage and phasor current.

    we know that phasor voltage, current and impedence can be represented by vector. we know phasor v is equals to the product of phasor i and impedence. the what is the process of multiplication? is it dot or cross product?
  8. M

    Superposition Rule and Phasor Current Calculations for a 50Hz Circuit

    Homework Statement The frequency is 50Hz (we've been told to always assume in our class that the frequency is 50Hz) and thus omega is 100pi. The Attempt at a Solution I don't have time to scan an image of my attempt (complete attempt) however what my query is: the way i went about to answer...
  9. T

    Engineering Circuits II, can someone check my equations ? Phasor Mesh Analysis

    EDIT I mean nodal, not mesh analysis xD http://img205.imageshack.us/img205/5931/omgt.jpg http://img694.imageshack.us/img694/2570/omg2p.jpg Are my are my equations correct? Here is the solution according to wolfram...
  10. F

    Negative Magnitude Phasor Presentation: Is Erasing the - Sign Correct?

    If you have a phasor that has a negative magnitude (ie -3<38degrees) what is the best presentation. I believed it was just erasing the - sign and adding or subtracting 180degrees. Correct me if wrong
  11. N

    Problem in transition from phasor to normal

    oiler formula says cosx+isinx but here they multiply by minus the imaginary part of the phasor representation the coefficient of sine is minus the imaginary part why??
  12. N

    Understanding Phasor Representation and Calculating Current in AC Circuits

    http://i47.tinypic.com/2mg2iyf.jpg i ant to find the current in phasor representation. i made found the Z total 210+j232.5 the current sourse is 2170 I=\frac{2170}{310+j232.5}=1454.56-j1610.4 but the calculation igives another result why?
  13. T

    Phasor Voltage and Voltage RMS value

    What's the difference between the two? RMS is divided by square root of 2?
  14. J

    Why a phasor consists of the magnitude of a voltage multiplied

    Does anyone know why a phasor consists of the magnitude of a voltage multiplied with a sinusoid? For instance, V_Scos(\omega t + \theta) I am searching all over the web, and cannot find a general explanation why. I've found some incomplete...
  15. J

    What is a Phasor? Explanation & Equations

    Homework Statement I am not sure what a phasor is. So when I looked it up on google, it simply said it was a sinusoidal function where A, \theta, \omega are time-invariant. I am not sure what would be good for, or any other relevant information. I also would like to know what v_x, V_s...
  16. A

    What is Time & Space Phasor? Difference Explained

    Can anyone please tell me what is time phasor and space phasor? and what is the difference bwt them ?
  17. R

    Homework Solution Understanding Phasor Diagrams for Circuit Analysis

    Phasor Diagrams?? Homework Statement Say I am given this circuit diagram. I have the recorded values on the voltmeter and ammeter. I can verify the power factor rating using these two values. But I also need to draw a phasor diagram for this circuit as well as two others which just have...
  18. N

    Drawing Phasor Representation for v(t)=20cos(200t+45°)+cos(200t)

    Draw the phasor representation for each of the following signals. Also write the signal as one sinusoid, v(t) = 20cos(200t+45°)+cos(200t) From this equation, do I have to turn to v(t) = A sin (ωt + φ) ? If yes, how can I convert it? Thank you.
  19. M

    Phasor representation question

    Guys, Quick one, When you do phasors for AC voltages and current... is it theVrms and Irms or can it be Vmax and Imax..? I mean the magnitude of them...I am bit confused
  20. Y

    Inerpretation of voltage and current phasor in transmission line.

    I have been trying to interpretating the voltage and current phasors in transmission line. I want to verify with you guys/gals here what my understanding. I am using only the voltage phasor as an example. I separate phasor V(z) into V(z)+ and V(z)-. I put the load at z=0 and V(z=0) at +r axis(...
  21. tony873004

    Understanding Phasors: Exploring the Concept and Its Applications

    My textbook's explanation doesn't do it for me, so I have to ask here. According to the textbook: "A phasor is an abstract vector whose y-component represents the value of a wave disturbance. The vector's magnitude equals the amplitude of the wave, and the angle it makes with the y-axis...
  22. A

    How Do You Apply the Phasor Method to Add Sinusoidal Functions?

    Homework Statement Add the formulas y1 = 5.2 sin(ωt), y2 = 8.3 sin(ωt+30°), y3 = 15.5 sin(ωt+60°) using the phasor method. Your formula should only have numbers and the variables ω and t. The formula must be accurate for any value of those variables Homework Equations Not sure...
  23. M

    Amplitude of field with phasor components

    Let's say I have a field (electric or magnetic or something) and it's time-varying so I choose to represent its components as phasors. Say the field is: \vec{F} = X\hat{x} + Y\hat{y} + Z\hat{z} where, X, Y and Z are complex numbers. Now, I want to find the amplitude of the field. If...
  24. G

    When does the current peak occur in an LC circuit with given values?

    Homework Statement An LC circuit includes a 0.025\muF capacitor and a 340\muH inductor. (a)If the peak voltage on the capacitor is 190 V, what is the peak current in the inductor? (b)how long after the voltage peak does the current peak occur? The Attempt at a Solution I've...
  25. D

    Phasor representation of plane wave propagation

    Homework Statement I was looking through my notes when I saw the following expression of a plane wave represented as a phasor A_{0}e^{i(\vec{k}\cdot\vec{r}-\omega t)} Now I can certainly understand a plane wave propagating along a given coordinate axis say, x or z, and the phasor...
  26. V

    Plotting Phasor representations of functions

    Homework Statement Plot the following for x = 0 to 8: This is part of a larger engineering problem, but I am stuck here, I have no idea how to plot a phasor. The original function is: y(x,\,t)\,=\,2\,cos\left(\frac{\pi}{6}\,t\,-\,\frac{\pi}{4}\,x\right) Homework Equations...
  27. P

    Exploring Phasor Analysis for Nonlinear Systems

    Hello, What happens when phasor analysis is applied to nonlinear systems? could someone explain me how it would work? :confused: Thanks
  28. V

    Find the phasor representation of an equation

    Homework Statement Find the phasors of the following time functions: (a) v(t)\,=\,3\,cos\left(\omega\,t\,-\,\frac{\pi}{3}\right) (b) v(t)\,=\,12\,sin\left(\omega\,t\,+\,\frac{\pi}{4}\right) (c) i(x,\,t)\,=\,2\,e^{-3\,x}\,sin\left(\omega\,t\,+\,\frac{\pi}{6}\right) (d)...
  29. Astronuc

    Phasor representation of AC voltage and current

    Phasor representation of AC voltage and current. I\,=\,5\angle{0^o}\,=\,5\,+\,j0\,A V\,=\,100\angle{30^o}\,=\,86.6\,+\,j50\,V in general V\,=\,A\angle{\theta^o}\,=\,A cos{\theta}\,+\,jA sin{\theta}\,V and similarly for I It is assumed that the angular frequency \omega is...
  30. H

    So, using the phasor approach, what is the solution to this circuit problem?

    [SOLVED] phasor approach question using phasor approach, determine the current i(t) in a circuit described by the integrodifferential equation: 4i + 8integral(idt) - 3di/dt = 50cos(2t + 75*) the right side is so easy to convert to phasor form, but how can i convert the left side or how to...
  31. M

    Transform this function into phasor form

    Tansform the following function of time into phasor form: 3 cos 600t - 5 sin (600t + 110) so I need to change the second term to a cosine term, any hints? or can I use a trig indentity that would make things easier?
  32. M

    Instantaneous Current Calculation in Phasor Form | Phasor Physics Problem

    Hello, came across this simple problem: Let w = 2000 rad/s and t = 1 ms. Find the instantaneous value of each of the currents given here in phasor form: a) j10 A; b) 20 + j10 A so for part a, I changed the current (0 + j10) to 10e^0 or simply 10, then my instantaneous value should be...
  33. V

    Phasor circuit problem: 1 resistor, 1 capacitor, 1 inductor, 1 Voltage source

    Homework Statement What value of \omega will cause the forced response v_0 in the circuit below to be zero? http://img248.imageshack.us/img248/1854/problem934ao5.jpg Homework Equations Phasor eqs. The Attempt at a Solution...
  34. K

    Convert Waves from Instantaneous to Phasor Form

    I need help in understanding how to convert waves from instantaneous form to phasor form: a wave expressed as E(z,t) = Eo * exp(-ax) * cos(wt - Bz) * ay How do i convert this wave to phasor form and determine its direction of propogation, phase velocity and wavelength? Thanks in advance...
  35. T

    Phasor Problem: Convert i(rt), i(ct) from i(t)

    for i = 0.4A cos (wt + 60) , how do we get i(rt) =0.35A cos(wt + 30) and then i(ct) = 0.2A cos(wt+ 120) ??
  36. T

    Understanding the Relationship Between Inductors and Resistors in an AC Circuit

    v(rt) = 125mV cos (wt + 60) R=250 ohms L = 250mH find i(t) in the circuit there is a inductor in series wif the resistor the answers i(t)=0.5 cos (wt+60) may i know why is it the inductor not using to form z and then only divide by v(rt) ??why only the resistor??
  37. T

    How Can Euler's Identity Be Applied to Write Phasor Equations v(t) and I(t)?

    for phasor, v = 20V e^(-j60) and i = 0.5A e^(-j30) how can i write them in v(t) and I(t) ?? pls help thanx
  38. S

    Solving 8-j3)5e^-jsomething Complex Phasor Problem

    I can convert sinusoids to phasors and vice versa if they are relatively simple, but I don't know how to deal with these two. (8-j3)5e^-jsomething. I was going to distribute, and make two vectors and find the resultant vector, but I don't think that's how to go about it. also Thanks ver much...
  39. L

    Interpreting Phasor and Sinor Diagrammes in Modulation: A Visual Guide

    What is Phasor and Sinor diagramme? What are they plotted agsinst? And how to interpret them? I have sample pic from my textbook.
  40. S

    Phasor Diagrams of Series Parallel RLC circuits

    Hi Guys! well! can anybody tell me the correct way of drawing phasor diagrams of Series-Parallel RLC circuits. I know how to draw for Series RLC and Parallel RLC but don't know WHEN it comes to SERIES-PARALLEL combined. Plz help me. Plus can u recommend me any website from where i can...
  41. E

    Solving Phasor Circuit: Finding Theta

    Hello, now we are in phasors and I am missing something in this problem: given a circuit of indep current source (5cos(wt)), R, L (with vL(t)) all in series, no values for them, although voltage across inductor vL(t) = 3cos(wt + theta), we need to find theta. So, by using impedance for...
  42. M

    Constructing Phasor Diagrams for Circuits

    Can anyone direct me to some good sites describing how to construct phasor diagrams based on different circuits? Didn't have much luck using search engines.
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