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. Franklie001

    Engineering RLC circuit -- Phasor Transfer Function calculation

    Good morning, I need some help solving those two question. I've attached my attempted solution below. Could i solve the transfer function any further? Thank you for your help
  2. P

    MATLAB Phasor diagram - how to check angle in matlab?

    I have a problem with checking angle in phasor diagram. I print my phasor diagram and I don't know how to check angle in window. Have somebody any idea how to search that? Maybe it is not possible and I need to add function in my MATLAB code to get result.
  3. Cassy85

    Create a Phasor Diagram Easily: Step-by-Step Guide & Helpful Tips

    Hi, I'm struggling to find out how to create a phasor diagram. I have attached a photo of the question any help would be greatly appreciated. This is what I have attempted so far. It's question 2b I am really struggling with. I'm not looking for the answers just looking for some direction...
  4. nobodyjusttrying

    Create a Phasor Diagram for Steady State Circuits

    So all we have to do is find the current and power distribution in the steady state circuit. Create a phasor diagram. I don't exactly know how to tell it in english, but i think there is a thing I called c. & p. paths.
  5. wcjy

    Circuits - AC circuits / phasor

    Hi, my school has no answer key provided. and would like to check if this is correct. Thanks!
  6. M

    Trouble Understanding Phasor to Time Domain Conversion Math

    This is a problem about converting from the phasor to time domain. I am having trouble following the math that the textbook is doing. I was thinking the final answer should be: i(d, t) = 0.20 cos(ωt + βd + 159◦) - 0.091 cos(ωt − βd + 185.6◦) emphasize the minus 0.091 instead of plus 0.091 as...
  7. Lars278

    RLC-circuits where phasor diagrams don't work

    When I studied Electronics I remember that there was some type of RLC-circuit where phasor diagrams could not be applied in order to find I, U and phi_u_i (φ_u_i). I've been searching the web to find that example. But I can't find it. Can anyone of you help me refresh my memory?
  8. B

    Engineering RLC Series Network: Impedance, Current, Power Factor, Phasor Diagram

    Hello. I have completed the following question. My answer: i) Circuit Impedance Reactance = XL = 2 x pi x F x L = 2 x pi x 50 x 0.15 = 47.12 Ohms Reactance of Capacitor = XC = 1/2 x pi x F x C...
  9. S

    [AC Circuit] How do we convert from the time domain to the phasor domain?

    In this example, We need to covert e2 & e5 to a form with imaginary number . we will obtain e2=j10 & e5=20 Can anyone explain how we got this?
  10. C

    What will the phasor diagram of this LCR circuit looks like?

    I know the current of capacitor and inductor must be parallel but pointing in opposite direction due to the fact they are connected in parallel thus having same voltage (please see attached screenshots). The current of resistor will simply be the sum of these two vectors, but what about its...
  11. R

    Adding Two Waveforms to find the final Phasor

    v(t) = 2cos(8t+180) + 10cos(8t+30) volts polar form = 2∠180 + 10∠30 convert to rectangular to add vectors = (2cos180 + i*2sin180) + (10cos30 + i*10sin30) = (-2 + i*0) + (8.66 + i*5) = 6.66 + i*5 find ⦵ and r of sum of vectors ⦵ = arctan(5/6.66) = 0.64 r = sqrt(5^2 + 6.66^2) = 8.33 V =...
  12. R

    Trying to type "I" with tilde on top (i.e. phasor notation) (MacOS)

    As the title says, I'm looking for a keyboard shortcut to type "I" with a ˜ The option+n shortcut does not work for I or V on MacOS. Thanks!
  13. MedEx

    Find the Driving frequency and phase angle for this R-C phasor problem

    Using the givens I found ωd=862 rad/s, and with some help I got tanϕ=-1 and Z=56.5685 ohms. But I can't figure out any of the other variables. I'm not even exactly sure what "driving frequency" is and I can't find an equation for it.
  14. MrsTesla

    I Phasor Addition Explained - Wave Physics

    Hello, In my lecture notes for Wave Physics, I have that phasor addition can be represented as a geometric progression. This is what was said in the lecture (see attachment). Can anyone explain me why are the mathematical contributions like that? (aka 5.22 in the attachment ) I've been trying...
  15. K

    I Using complex numbers or phasor transform to solve O.D.E's

    Hi particular solution only. As an example of what I am talking about, this method works for this DE: $$ 4y' + 2y = 10\cos(x) \\ \\ 10 \cos(x) = \Re( 10 e^{j(x)} ) = \Re(e^{j(x)} \cdot e^{j(0)} ) \rightarrow \text{complex number that captures the amplitude and phase of 10 cos x is} \\ 10...
  16. Peter Alexander

    Understanding Transformer Phasor Diagrams

    Hello everyone! I'm currently studying transformers and a task related to phasor diagrams shows up. I'm having lots of problems with comprehension of the subject, so I'd like to ask for some help. I don't understand how the phasor diagram given as a solution could possibly be drawn out of the...
  17. J

    Power System Fault Phasor Diagram

    Homework Statement Homework Equations If load is inductive current lags voltage. If load is capacitive voltage lags current The Attempt at a Solution Current lags voltage since wire is inductive. So IF1 lags VF1 and IF2 lags VF2 But book says answer is C Why should VF1 lag IF1? This will...
  18. BryanDorais

    How do I find voltage at time t given a voltage phasor?

    This is a problem from my midterm that I'm trying to understand before my final. The question is; A voltage phasor is given by V = 12∠70° and the frequency is 60 Hz. What is the time-domain voltage at t = 1 ms? a. 1.47 V b. 5.11 V c. -0.335 V d. -4.73 V As far as i know, the only equation...
  19. J

    Autotransformer phasor diagram

    I'm studying Auto Transformer phasor diagram, and am having some doubts. I'd be grateful if someone could help me out with them. Book has equation: I understand that using Kirchoff's law we get minus sign for (I2 - I1) term, but shouldn't it be positive as per concept? Negative sign means the...
  20. doktorwho

    Help understanding phasor solution

    Homework Statement From the given circuit and provided information draw a phasor and calculate the inductance. Homework Equations 3. The Attempt at a Solution [/B] The paper was given to me at class as a solution to our homework and i can't understand how they drew the phasor and drew the...
  21. Ravensight

    Engineering Finding unknown Phasor in a series-parallel circuit

    So this is a "bonus" question from a past final exam for my Electrical Circuits course. I've spent a good few hours trying to solve it but haven't really had much luck. Any method can be used I figured if I found the voltage of the known XL, it would be equivalent to the voltage of the unknown...
  22. Cocoleia

    Working with phasors (Circuits, such as complex power)

    Homework Statement I am going over examples in my textbook and I came across this: I don't understand how they converted 18.265 at angle of 39.9 to 14.02+j11.71 Homework Equations I know how to convert from the imaginary numbers into the angle form, usually I use: Is there another equation...
  23. TheBigDig

    Engineering Finding Phase Difference in an RC circuit

    Homework Statement Homework Equations ##V = ZI## ##Z_R = R## ##Z_C = -\frac{j}{\omega C}## ##Z = \sqrt{R^2 + (\frac{1}{\omega C})^2}## ##P_{av} = \frac{1}{2}V_m I_m cos(\phi)## ##\phi = arctan(\frac{-1/\omega C}{R})## ##\Delta \phi = \phi _1 -\phi _2## The Attempt at a Solution I've found...
  24. C

    Converting phasor to time domain

    Homework Statement Homework EquationsThe Attempt at a Solution I am extremely confused. Everywhere I go to look on how to convert phasors into time domain I get a different answer. I am trying to convert -j to the time domain. My notes says to find the Im(phasor). I have explained in the...
  25. T

    Electromagnetic wave phasor conversion

    Homework Statement Homework EquationsThe Attempt at a Solution So I was given the electromagnetic E field equation in phasor form and I converted it to sinusoidal form. Is it correct ? Also will it be a reflected wave since we have (wt+Bz) and not (wt-Bz) ? Also will it be circularly...
  26. C

    Finding Steady State Amplitude of Voltage Across Load Resistor

    Homework Statement Find the steady state amplitude in volts of the voltage across the load resistor Homework Equations V source = 4sin4t Resistors = both 1ohm Cap = 1.414F Inductor = 1.414H The Attempt at a Solution I converted to phasor domain first, then applied voltage division. Voltage...
  27. whatphysics

    How do you work out simultaneous eqns w/ complex numbers & phasor

    I'm having trouble figuring out to get the answers from the 2 equations. The phasors and complex numbers confuse me. Do I need to change the phasor form? How do I go about doing this thanks! (Not homework question I am trying to figure this for my exam!)
  28. smstepanic

    Current of Phasor going in CCW direction

    Hi, I feel I have solved this problem correctly (solving for vo(t)), however since the current is going in the ccw direction, would this make the current -5cos(10t - 45) versus 5 cos(10t -45)? This may be a simple question, so I am just making sure. Thanks!
  29. C

    Converting phasor back into time domain

    Homework Statement Find Amplitude of Steady-state voltage across capacitor Homework EquationsThe Attempt at a Solution I'm at the very last step of changing it back into the time domain to obtain my ampltiude. I was planning on getting it into the form a + bj, then using trigonometry and...
  30. Z

    How can RMS current be phasor?

    If RMS current is equal to the value of the direct current that would produce the same power dissipation in a resistive load, how can it be phasor?
  31. J

    Engineering Synchronous Motor Phasor Diagram

    It's not really a problem but I was studying Sync Motors for assignment and didn't understand few things. 1. Homework Statement http://s1320.photobucket.com/user/ajaytulsiani/media/-%20ia_zps8oujbzrh.jpg.html http://s1320.photobucket.com/user/ajaytulsiani/media/synch_zps3bry0aah.jpg.html In...
  32. kostoglotov

    Difference between phase angles

    Homework Statement [/B] imgur: http://i.imgur.com/9ktFGSs.pngHomework EquationsThe Attempt at a Solution [/B] I came up with both 150 and 210 as the difference between the phase angles. I chose 150. If you draw the vectors and compare their angles, the angular difference between them could...
  33. L

    Synchronous generator phasor diagram

    1. Problem Statement: A 4-pole, star-connected, 50 Hz, 11kV, 40 MVA turbogenerator, with a synchronous reactance of 0.8 p.i., is connected to a power network. This power network can be represented by 11-kV infinite bus with a series reactance of j 0.5 Ω. A voltage regulator adjusts the field...
  34. X

    Phasor angular velocity for a triangle wave?

    What would the angular velocity for a phasor be for a triangle wave? I think it would vary sinusoidally but I can't find an expression
  35. Titan97

    Phasor algebra in AC circuit analysis

    Homework Statement Find the peak value of current through the AC source of the following L-C-R circuit, if peak voltage is ##V_0## and angular frequency is ##\omega_0##. Homework Equations I have learned Vector algebra and calculus (single variable). I was taught how to use phasor diagrams...
  36. MacLaddy

    Engineering Phasor Circuit Analysis Homework: Understanding Incorrect Answers | MacLaddy

    Homework Statement Hello folks. I had a recent midterm where I got a problem wrong, but I'm not sure I understand why. I am hoping someone here can shed some light. Please see the attached circuit diagram.Homework Equations Phasor notation stuff... I am correct on all except one sign. Please...
  37. N

    Engineering Calculate phasor of voltage in circuit

    Homework Statement Calculate phasor of the output voltage (Vout). The circuit is powered by a sine wave voltage source (Vs) with amplitude=10V and frequency=1000Hz. Homework Equations Voltage= Current*Impedance (V=IZ) Z(R) = R Z(C) = 1/jwC i(t) = Acos(wt - phi) V(out)=[Z(C) / (R+Z(C))]*Vs The...
  38. B

    Please help with A/C calculations and phasor diagrams

    I have completed the questions in the attachment I just need someone to tell me if they are correct and I'm doing them right. Thanks.
  39. T

    Three phase phasor proof or simplification

    So I'm really rusty on phasors, I was reading that a space vector current was i(t) = I(cos(wt)<0 + cos(wt - 120)<120 + cos(wt - 240)<240 ) = 3/2 * I < wt and I couldn't figure out how that could be so (still can't, please help) So I tried to go back to basics and I went back and read: A =...
  40. R

    Engineering Instantaneous Current in single phase circuit

    Homework Statement SOURCE: v(t) = (311)cos(314t) [v] IN SERIES WITH: R = (0.3) [Ω] L = j(0.7) [Ω] "load" = 2.5 + j(1.0) [Ω]Homework Equations Find the instantaneous current, and the phasor current. The Attempt at a Solution (1.) I first found the frequency of the source: (314) / (2*pi) ≈ 50...
  41. bananabandana

    Superposition of Two Travelling Waves, Different Amplitudes

    Homework Statement I'm looking at an E&M textbook - "Time-Harmonic Electromagnetic Fields". They state: "A more general ##x ## polarized field is one consisting of waves traveling in opposite directions with unequal amplitudes - i.e : (1) $$ E_{x} = Ae^{-jkz} +Ce^{jkz}$$ Let ## A ## and...
  42. S

    Understanding Phasors: How to Sketch a Voltage Phasor in Polar Form

    Hello Excuse me, but how do I sketch the phasor of a voltage that it's V=5cos(10t+30degrees) and how the V=5sin(10t+30degrees) ? I know that these can be converted as the R<angle polar form, with R being the Vmax, ie the 5, and the angle the phase. But what doesn't it matter if I have cos or...
  43. B

    Need help proving an equation for power loss in a dielectric

    Homework Statement 2. Homework Equations [/B] I am trying to prove the equation $$ \frac{\bar{P}}{V}=\frac{1}{2}E_0^2\sigma_{AC} $$ which can be rewritten as $$ \begin{align} \frac{\bar{P}}{V} &= \frac{1}{2}E_0^2\sigma_{AC}\\ &=\frac{1}{2}E_0^2\ \omega\ \epsilon_0\ \epsilon^{''}_r\\...
  44. X

    Engineering Solving unkown impedance in circuit

    Homework Statement Homework Equations V=IZ The Attempt at a Solution So my plan is as follows: Find the current through the 1 ohm resistor, multiplying this by the combined impedance of the capacitor & 1 ohm resistor. Now I know the voltage across the unkown impedance Z. Subtract this...
  45. X

    Engineering Solving phasor circuit with unknown dep. current src

    Homework Statement Homework Equations V=IR The Attempt at a Solution I try to simplify the circuit by combining the capacitor and 2ohm resistor in parallel, Z = 1-j. Then I add the inductor to get Z = 1. Knowing the current across the resistor, 2(0d) I find the voltage across the 5 ohm...
  46. X

    Engineering Phasor Circuit Analysis Homework: KCL & Z Equations for Capacitors"

    Homework Statement (Note, my answer below is also wrong. I've attempted this problem for about 1 hour now and I can't figure it out.) Homework Equations KCL (Kirchoffs Current Law) Z for the capacitor, Z = 1/(jwC)[/B]The Attempt at a Solution I'm using KCL at V1 with the following...
  47. ashtadmir

    Phasor analysis of transverse wave on a string

    The way we have a phasor analysis for a point mass executing un-damped simple SHM, is there something like that for transverse waves on a string. According to me if we fix the position then we can focus on the isolated SHM at that particular position. Is there any way in which I can relate the...
  48. R

    Phasor representation for a mass and spring

    Hi, While writing the Fourier representation for the spring-mass system, we have the equation: (-jωm+B-S/jω).U(jω)=F(jω) with F,U,m,B and S being the force, velocity,mass, damping coefficient and spring constant respectively. From this equation, is it right to infer that : 1) Force lags the...
  49. A

    Uniform plane wave parallel/perpendicular phasor problem

    Homework Statement Homework Equations lambda= 2*pi / k Ei(z), Ei_perpendicular (z), Ei_parallel(z) eq. epsilon_r1=1, epsilon_r2=2.25 eta_1=120*pi, eta_2=80*piThe Attempt at a Solution I having trouble understanding some parts of this problem. i get k1=3.61, k2=5.42 and for d)...