# What is Phasors: Definition and 75 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. ### B How can scalars like voltage, impedance, etc. be added like vectors?

So we learnt about the different types of circuits and their behaviour when connected to an alternating current source. (DC was treated as an AC with 0 frequency and/or infinte time period). For purely inductive and purely capacitive circuits we were shown the derivation and why things are the...
2. ### Converting from sin to cos appropriately with phasors

My transmissions line class often features problems where the voltage is expressed as a sin, not a cos. Obviously a phase shift of pi/2 is sufficient to convert between the two. However, I have trouble understanding when adding pi/2 is appropriate as opposed to subtracting pi/2. As per my...
3. ### Engineering AC Circuit Phasors: Find I1, I2, I3

Summary:: Hi, I tried attempting this problem in alternating current in order to find out the phasors as complex numbers, and I would be more than grateful if someone could peer review it, and confirm my calculations (Please see below both the Figure and the calculations) Please find attached...
4. ### Inferring Shape of Phasors in Multi-Slit Diffraction

I know that phasors of a single-slit diffraction form a closed polygon or circle, but how could we infer the shape when phasors generated by slits of a multiple-slit barrier?
5. ### Calculating phasors from sensor readings

Hi! I am working on a project (hobby basis) and with limited EE background. I wish to make a polar plot, showing the current and voltage phasors for each phase (unbalanced 3-phase, 3 wire system (IT system), se picture below.). I have obtained the following readings (instantaneous values)...
6. ### Resultant amplitude of 6 phasors

Homework Statement This is a problem from one of my students, he is taking an undergrad module in optics. Most of the question is fine but I cannot see a neat solution to part ii Homework Equations These are the equations for the topic, but I am not sure if we are missing the relevant...
7. ### Sinusoids as Phasors, Complex Exp, I&Q and Polar form

Hi, I am going around in circles, excuse the pun, with phasors, complex exponentials, I&Q and polar form... 1. A cos (ωt+Φ) = Acos(Φ) cos(ωt) - Asin(Φ)sin(ωt) Right hand side is polar form ... left hand side is in cartesian (rectangular) form via a trignometric identity? 2. But then...
8. ### What does this voltmeter measure?

Homework Statement Consider the following circuit where i(t) is sinusoidal and exists across both components. (1) is an inductor and (2) is a capacitor. The ideal voltmeters measure effective value. What is the value measured by V2: [![enter image description here][1]][1] [1]...
9. ### KCL with phasors: how to proceed knowing effective values

Homework Statement I have the following problem. Consider a circuit node where 3 sinusoidal currents with the same frequency converge, i1 i2 and i3. Knowing that the effective values of i1 and i2 are I1ef=1A and I2ef=2A. What can we say about I3ef: Options: $$(a)1A \leq I_{3ef} \leq 3A$$...
10. ### 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...
11. ### How to operate in Angle Notation (Electrical Engineering)

Background info (Not actual question): So I've been gone a week from university and I've missed a lot of content, one particular thing that boggles me is this new method to operate with vector magnitudes and their angles. The operations surprised me with the speed they were done. I did ask a...
12. ### Revisiting Phasors: Understanding the w in VL

Homework Statement Hi, I'm revisiting phasors again. This is one of the topics I've always struggled with. Every time I do a new module, they change a lot of the convention. I've been using Schaums outline of electric circuits recently to get refreshed. I'm just confused on this one part...
13. ### 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!)
14. ### Engineering RL circuit Q. I must be missed something simple

Homework Statement Homework EquationsThe Attempt at a Solution I would show my working, but honestly, I'd really just like a hint as to how to begin, because I've tried multiple different things and just gotten tangled up in multiple equations that are way more complicated looking than the...
15. ### Is Electric Current a Scalar, Vector, or Constrained Vector?

what is electric current...a scaler or vector?? ...well I personally believe that it is somewhere in between the two extremes (what is not 0,need not be an 1 either :oldbiggrin: ) ...particularly because of the strange similarity we see in vector addition and phasor addition)...some people...
16. ### Relativistic Time & Mass-Energy Phasors

I’m trying to get a better handle on reconciling the concept of time as it relates to the quantum wave function and the relativistic 4-momentum. To put it simply, do we look at the coefficient of the time variable in each as something separate from the time variable itself, or do we treat these...
17. ### How are phasors obtained from real values in AC?

Ok, so I know phasors are based on Euler's Formula: ej*(X+phi) = cos(X+phi) + jsin(X+phi) But how do we use real value like V(t) = Acos(V+phi) in Euler's Formula? V(t) has no imaginary component, so how can we write the phasor of this as A<phi, where phi is the angle between real and imaginary...
18. ### Finding i(t) in a Circuit with Phasors: Introductory Exercise

Homework Statement In this circuit, find i(t), knowing that v_s= 2 \cos \left(w x+\frac{\pi }{2}\right), and that, at the source's frequency, X_C= -1 Ω and X_L = 1 Ω. Homework Equations Basic phasors and dividers equations. Z_C = jX_C Z_L = jX_L The Attempt at a Solution I used dividers...
19. ### 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 =...
20. ### Engineering Electrical Engineering - AC Circuits Phasors

Homework Statement Please see attached image 1 and image 2 Homework EquationsThe Attempt at a Solution Alright so I believe I solved part a correctly. It was very easy. (A) 5 * phasor of 30 degrees However it's been a while since I took circuits 1, so I'm struggling a bit with part (b)...
21. ### Why do we use i to represent phasors and/or vectors?

Somestimes, vectors (e.g <3,4>) are represented with a real and imaginary component (3 + 4i). When expressing wave phasors as vectors, this is usually the convention. Insofar as phasors and waves go, what rationale does the convention have? If I had to superimpose two waves together, and...
22. ### Phasors: How to go from Re{} to Re{}+Im{}

I understand that V=cos(wt+\phi)=Re[e^{j(wt+\phi)}] But when doing calculations (like loop voltage analysis or junction current analysis) you're just using V=e^{j(wt+\phi)} (where all of the e^{jwt} will cancel out and you're just left with the phasors) Example: A_se^{j\phi...
23. ### 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...
24. ### MHB Reviewing Phasors: When to Add +/- 180 in $\tan^{-1}$?

I'm reviewing phasors (in circuits) and my prof wrote that if you're taking the inverse tangent, $\tan^{-1}{\frac{b}{a}}$ where $a$ is negative, you need to add $+/- 180$. Now I understand that the inverse tangent is defined between $-\pi/2$ to $\pi/2$ for invertibility, etc, but adding or...
25. ### Vout = (a+jb)Vin, what do A and B stand for?

Homework Statement I was given a graph with two waves on it, the input and output wave. I found the frequency of the waves, change in magnitude and change in phase. The last question asks me to write the transformation from input to output as a phasor and he gave the relevant equation below...
26. ### Engineering Circuit Analysis using Phasors

Do I have the right idea? I'm not getting what is in the solutions manual but it's been wrong on past chapter and I'm beyond frustration.
27. ### Find current using mesh analysis question?

Homework Statement We have the circuit in the figure.I have to find Io. Homework Equations Mesh current analysis. The Attempt at a Solution The first mesh is i1 and the second one is i2. We have a supermesh here.Supermesh results when two meshes have a (dependent or independent)current...
28. ### The average power consumed -- where is my mistake

Homework Statement We have the circuit in the figure.I have to find the average power consumed by all the elements and the source. Homework Equations P=0.5*(I^2)*R P=-VmImcosθ/2 The Attempt at a Solution The inductor consumes zero inductive power. I apply nodal analysis at node Vo We have...
29. ### Engineering Nodal analysis question -- circuit analysis

Homework Statement We have the circuit in the figure.I have to find the current i using nodal analysis Homework Equations 1/6 F =-3j 1/2 F= -j 1/2 H= j The Attempt at a Solution So we have the equations Node V1 : [(7-V1)/(4-3j) ]=[ V1/3 ]+ [(V1-V)/-j] Node V : [(V1-V)/-j] =(V )+ (V/j) In...
30. ### Nodal analysis exercise,are my equations correct?

Homework Statement We have the circuit in the figure.I have to find v using nodal analysis only. Homework Equations Converted 1/6 F to -3j and 2sin2t to -2j. The Attempt at a Solution In node v1 we have the equation 6= -12+ [v1/2] + [( v1-v)/1] In node v we have the equation 2j+ [(v1-v)/1]=...
31. ### Obtain Expression For Voltage Across Capacitor

Homework Statement A voltage source given by ##v_s(t)=25cos(2\pi\times10^3t-30^\circ)## is connected to a series RC load. If R = 1MOhm and C = 200pF, obtain an expression for ##v_c(t)##, the voltage across the capacitor. Answer known to be: ##v_c(t)=15.57cos(2\pi\times10^3t-81.5^\circ)##...
32. ### Calculate Phasors of Current with 3 Capacitors

Is it possible to calculate phasors of current through 3 different capacitors in a circuit? The Supply voltage is given and the frequency is given. I was also given all the 3 capacitor values. Two of the capacitors are connected in parallel and the result of that in series with the remaining...
33. ### Quick question, phasors and impedance

Please see attached On line S=0.5*V*I why is the minus sign removed from in front of the "I" angle. 25.38 specifically. Could is be a typo? http://imgur.com/eUmEovo
34. ### What is the significance of complex vectors in electromagnetism?

I've recently began a course on electromagnetism and have started dealing with complex vectors. I have a couple questions to ask: Regarding the general concept of complex vectors, I am curious what these actually represent. Refer to attached equation. Am I correct to believe that this...
35. ### MHB Convert V: 10< 90 Degrees + 66 - j10V at 10k Rads/s

Question: Convert V = 10< 90 degrees + 66 - j(10 V) at angular frequency = 10k rads/s. I am stuck here 10(cos(90)+ j(sin(90)) + 66 - j(10) which would then be: 0 + j + 66 - j(10)
36. ### Steady State Circuit Analysis with Phasors

Homework Statement Hello everyone! I have the following circuit to solve, and my result is a bit wrong... can you tell me please where's the mistake? E=10sin(1000t) Find the current delivered to the circuit. Find the equivalent impedance of the circuit. Find the equation of the current and...
37. ### Adding sinusoidal functions using phasors

Homework Statement Homework Equations The Attempt at a Solution $$3cos(20t+10°)-5cos(20t-30°)\\ =3\angle 10°-5\angle -30°\\ =-1.376+3.0209j\\ =3.32\angle -65.51°$$ In the last step, the textbook actually got ##3.32\angle 114.49°##. I checked both answers and it seems that the textbook's...
38. ### Question on phasors at boundary of oblique incidence.

A plane wave travels in ##\hat k_I=\hat x \sin\theta_I+\hat z \cos \theta_I## direction hitting a boundary formed by xy plane ( z=0). The incidence wave is in the plane of incident formed by xz plane where y=0. We let ##\tilde E_I(\vec k_I)= \hat x E_{I_x}+\hat y E_{I_y}+\hat z E_{I_z}...
39. ### Analyzing a Circuit with Phasors: Determining Inductance and Resistance

Homework Statement When the circuit shown in the figure is at steady state, the mesh current is i(t) = 0.3255 cos(10t + 133.3°) A Determine the values of L and R. Zc is the impedance of the Capacitor ZL is the impedance of the Inductor I1 is the current in the top loop I2 is the current in...
40. ### Engineering RLC parallel circuit phasors and current

Homework Statement Sorry for the stupid question, but I want to be sure whether everything is correct. Here is the problem, I think I managed to do all the parts. 2. The attempt at a solution a)ω=2∏f; ω=4000∏ or 12566.37 rads b)Xl = ωL = 4000∏x0.004=50.27Ω c)I1=R x Vac I2=Xl x...
41. ### What are phasors and how do they relate to determining the wavelength of a wave?

Homework Statement My physics text states: "We can represent a string wave (or any other type of wave) vectorially with a phasor." Now, for phasors the amplitude and angular frequency are given. If this is the case though, how is k, the angular wave number (and hence the wavelength)...
42. ### Sinusoids and Phasors (Micro-Cap)

Homework Statement Hi, I've been trying to figure this out for a while, its really annoying because it should be straight forward but its troubling me a lot. The exercise is a practical on Sinusoids and Phasors. We are given the circuit and have to first calculate the voltage and...
43. ### Engineering Solving a second order circuit with phasors

The question requests that I solve the circuit below for v0(t). I'm solving for the voltage over the inductor. I'm getting a result that's close to what I expect, however I think the phase angle of the voltage is slightly off (some friends of mine said they all got 46°, whereas I am consistantly...
44. ### Find Power w/ Phasors: V=IZ in Electrical Engineering

This is not necessarily a HW problem but more me just trying to understand a concept. Why can you multiply phasors together to find Voltage using V=IZ but you can't multiply a current phasor with a voltage phasor to find a power phasor. Instantaneous power is Voltage and Current functions...
45. ### Using Phasors to Graph Intensity vs Angle (4 slits)

3.a) Use phasors to sketch the intensity vs. angle for a 4-slit interference pattern (identical width and separation d=5 microns, wavelength =0.5 microns.) b) On the same angular scale, draw the intensity pattern if the top two slits are covered. c) The intensity pattern if the bottom 2...
46. ### Laplace Transforms and Phasors in Circuit Analysis

So last semester, I had a Circuit Analysis course where I learned about phasors. Basically, when dealing with AC circuits, I should convert everything to the frequency domain where X = j\omega L and X = \frac{1}{j\omega C}. I feel like I understood this part really well. However, in Circuits...
47. ### Understanding Phasors and Complex Numbers in Harmonic Functions

Homework Statement What are the phasors F(t) and G(t) corresponding to the following functions: f(t) = Acosω1t and g(t) = Acosω2t Draw the phasors on Argand diagram as well as F(t)+G(t) at t = \pi/(2ω1) and from the diagram get f(t)+g(t) as a cosine identity in the simplest form...
48. ### Solve V = 5 + 12*j in Form v(t) = A*cos(w*t) + B*sin(w*t)

Homework Statement If V = 5 + 12*j then write v(t) in the form v(t) = A*cos(w*t) + B*sin(w*t) w = 10000 rad/s Homework Equations N/A The Attempt at a Solution I can easily put it into the form v(t) = C*cos(w*t + phi) and I can probably get the above form using a trig identity (haven't...
49. ### Circuits: Mesh Analysis with Phasors

Homework Statement I am supposed to use mesh current analysis using the following circuit diagram which is in the phasor domain: Homework Equations KVL The Attempt at a Solution Let's number these meshes from left to right 1,2,3. Here is what confuses me: If take a look at...
50. ### Rms current, complex area, phasors

A lot of questions: http://img846.imageshack.us/img846/4963/capture3jpg.jpg http://img861.imageshack.us/i/captureh.jpg/ Find i2 Solution: http://img847.imageshack.us/img847/3773/capture2g.jpg Sorry for image spamming, i thought i should give you exact numbers and all so u can...