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.
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...
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...
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...
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?
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)...
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...
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...
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]...
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:
$$(a)1A \leq I_{3ef} \leq 3A$$...
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...
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...
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...
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!)
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...
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...
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...
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...
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...
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 =...
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)...
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...
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...
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...
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...
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...
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...
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...
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...
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]=...
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)##...
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...
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
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...
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)
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...
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...
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}...
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...
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...
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)...
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...
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...
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...
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...
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...
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...
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...
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...
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...