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.
Homework Statement
An emf Vosinwt is applied to a circuit which consists of a self inductance L of negligible resistance in series with a variable capacitor C. The capacitor is shunted by a variable resistance R. Find the value of C for which the amplitude of the current independent of R...
Hi,
I have the following circuit:
[PLAIN]http://img252.imageshack.us/img252/9470/phasor.png
I need to find the current i(t).
I have come to a point where i don't know how to proceed.
I have the inductor and resistor in series.
40 +j120 in phasor form 126.5\angle 71.56
which...
Homework Statement
Evaluate the following complex numbers (results in rectangular form):
\frac{10 + j5 + 3\angle 40^{\circ}}{-3 + j4} + 10 \angle 30^{\circ}
Homework Equations
I know that the solution is:
8.293 + j2.2
But i get a different answer.
The Attempt at a Solution
Convert into...
Homework Statement
x(t) = 2sin(\omega0t + 45o) + cos(\omega0t)
Express x(t) in the form x(t) = Acos(\omega0t + \phi)
The Attempt at a Solution
I don't really know when to begin; I can't find anything about it in the textbook.
Ok, I'm trying to wrap my head around phasor notation. I think part a is correct, not sure of the difference for subtraction and converting phasor to polar notation. Any help is appreciated!
Problem:
For A=5<36.9 and B=5<53.1
a)Calculate the sum A+B
b)Calculate the difference A-B...
Homework Statement
I'm working on a problem where I have to add two phasors together. The problem is, the real parts cancel out and I can't figure out how to express the phase because arctan(y / 0) isn't defined.
Homework Equations
x1 = 10<45 degrees
x2 = 10<135 degrees
x1 + x2 =...
I'm having a bit of trouble understanding how phasors/complex numbers are used to solve circuits which include capacitor, inductor and resistor components.
Has anyone come across video lectures/youtube tutorials/websites that provide comprehensive solutions to a whole bunch of...
Hi everyone!
I understand the general concept but I came across a function such as:
E(t)= 0.1 sin[10(pi)x]cos[6(pi)10^9t - Bz]
I'm supposed to combine them using phasors and I'm really confused how to
a) Transform it into the exponential function
b) Transform it back in the...
For the following, I was wondering if someone could help me determine the imaginary part of the complex number:
Im<GVV* - j\omega CVV*>, where V* is the complex conjugate of V.
I was thinking the imaginary component would be -\omega CVV*. But I am reluctant on the conclusion, because I am not...
Current and Phasors
Statement:
A simple circuit is given, such that the AC power source "V" is in parallel with a resistor "G" (why would it be denoted by G instead of R?), and also parallel with a capacitor "C".
Relevant equations:
Converting the circuit to phasors, the current from the...
I would attempt to solve these questions with "relevant equations", but my questions simply derive from an attempt of understanding class notes. If someone could attempt to help my understanding, that would be great. I've attached the PDF file that contains my corresponding questions...
what's a phasor? What's the phasor domain?
I've worked with them in my courses and I can move from the time domain to the phasor domain, but I still don't quite intuitively get what a phasor is.
In physics, we move between the frequency domain and time domain easily, but they're both...
I'm having some difficulty Solving this partial fraction:
(3.84e7)/(s(s^2+6.4e4s+1.6e9))= (3.84e7)/(s(s-3.2e4+j2.4e4)(s-3.2e4-j2.4e4)
how do u find the angle?
I know the equation but I don't know how to find the B with it conjugate.
eq: 2B/_theta
but I don't know how to...
Ok so i just want to clear up something about phasors and just circuit input functions in general. So based on the imaginary and real graph, where imaginary is like the y-axis and the real is the x axis, when let's say a circuit falls on the imaginary axis is it considered a stable circuit? Do...
Hi all.
If I have a current going from A to B with a phase of 0.78 (radians) at time t, and a current going from B to A with a phase of 0.78+Pi = 3.93 at the same time t, does this mean that the currents are going the same way?
Thanks in advance.
Niles.
Homework Statement
Two "waves", characterized by cosx and cos^2(x/2) interfere. Using phasors or complex numbers or trigonometry as necessary, aggregate "cosx + 2cos^2(x/2)" - i.e. rewrite as a single cosine.
Homework Equations
I was told that there is an error in the way this questions...
Homework Statement
use phasors to evaluate the steady-state solution to the equation f'' + 1.5f' + f = Ce^2tj
Homework Equations
The Attempt at a Solution
let f = Ce^2tj (this is a 'trial solution', i think)
f' = 2tCe^2tj
f'' = 4(t^2)Ce^2tj
therefore 4(t^2)Ce^2tj + 3tCe^2jt...
1. Find the sinusoids represented by these phasors:
(a) I = -3 + j4 A
3.
well to convert first to polar they got the following
they didnt show their steps:
I = 5 <126.87
then they said
i(t) = 5 cos(wt + 126.87)
What I don't get is the fact that how they got 126.87...
Homework Statement
Let's say I have
(1) 6<-9
and
(2) 6<189
I don't have a problem drawing the phasors out, however, I am having a bit of difficulty determining how to 'read' the diagram and tell how one leads/lags the other.
In the example I've given, I draw out the phasors but...
http://img247.imageshack.us/img247/7035/problemso9.jpg
Ok so I have to do mesh-current analysis and I think I'm doing it correctly but my answer doesn't match the one given. This has to be done using phasors.
I labeled my meshes from left to right 1, 2, and so on.
Mesh 1:
33.8 = 1I1 + j2I1 +...
Homework Statement
I can't post pictures as I do normally, so you'll have to deal with the cumbersome attachment method! It's just a simple RC circuit. Resistor on top, capacitor on right side with the sinusoidally varying voltage source on the left...
Ok i have been given two trigonometric functions and asked to give them as phasors, and then calculate the average power supplied from this.
v = 311 sin (200t+7\circ) V
i = 14 sin (200t - 16\circ) A
I'm used to the trigonometric functions being in the cosine form, what difference will this...
Resistance and Phasors?
Hi I am a Mechanical engineer but I am taking a module in electrical, which isn't my strong point. Please can someone explain the differnce between bilateral and unilateral resistance and what is a good website to help me understand phasors and sinusoidal quantities...
Hoping someone can give me a nudge in the right direction for this..ive tried searching the net and unless I am putting in the wrong keywords, there doesn't seem to be much useful material out there for this. I need to add together two phasors to find the resultant amplitude and phase of each...
Something's bugging me. Suppose we take kvl around a loop in a circuit, we have:
v1(t)+v2(t)+...=0
Suppose v1, v2, v3(t) are all sinusoidal (they can be written as Acos(wt+s)).
So we have
A1cost(wt+s1)+A2cost(wt+s2)+...=0
Suppose we replace all of them by their phasors, this should...