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.
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
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.
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...
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.
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...
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?
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...
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...
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.
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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!)
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!
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...
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...
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...
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...
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...
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...
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...
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
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...
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}$$
Let ## A ## and...
Hello
Excuse me, but how do I sketch the phasor of a voltage that it's V=5cos(10t+30degrees) and how the V=5sin(10t+30degrees) ?
I know that these can be converted as the R<angle polar form, with R being the Vmax, ie the 5, and the angle the phase.
But what doesn't it matter if I have cos or...
Homework Statement
2. Homework Equations
[/B]
I am trying to prove the equation
$$
\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\\...
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...
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...
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...
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...
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...
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)...