# 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. ### 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. ### 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. ### 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. ### 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. ### Circuits - AC circuits / phasor

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

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15. ### 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...

45. ### 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...
46. ### 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...
47. ### 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...
48. ### 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...
49. ### 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...
50. ### 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)...