What is Phase angle: Definition and 83 Discussions

In physics and mathematics, the phase of a periodic function


{\displaystyle F}
of some real variable


{\displaystyle t}
(such as time) is an angle-like quantity representing the fraction of the cycle covered up to


{\displaystyle t}
. It is denoted


{\displaystyle \phi (t)}
and expressed in such a scale that it varies by one full turn as the variable


{\displaystyle t}
goes through each period (and


{\displaystyle F(t)}
goes through each complete cycle). It may be measured in any angular unit such as degrees or radians, thus increasing by 360° or


{\displaystyle 2\pi }
as the variable


{\displaystyle t}
completes a full period.This convention is especially appropriate for a sinusoidal function, since its value at any argument


{\displaystyle t}
then can be expressed as the sine of the phase


{\displaystyle \phi (t)}
, multiplied by some factor (the amplitude of the sinusoid). (The cosine may be used instead of sine, depending on where one considers each period to start.)
Usually, whole turns are ignored when expressing the phase; so that


{\displaystyle \phi (t)}
is also a periodic function, with the same period as


{\displaystyle F}
, that repeatedly scans the same range of angles as


{\displaystyle t}
goes through each period. Then,


{\displaystyle F}
is said to be "at the same phase" at two argument values



{\displaystyle t_{1}}



{\displaystyle t_{2}}
(that is,








{\displaystyle \phi (t_{1})=\phi (t_{2})}
) if the difference between them is a whole number of periods.
The numeric value of the phase


{\displaystyle \phi (t)}
depends on the arbitrary choice of the start of each period, and on the interval of angles that each period is to be mapped to.
The term "phase" is also used when comparing a periodic function


{\displaystyle F}
with a shifted version


{\displaystyle G}
of it. If the shift in


{\displaystyle t}
is expressed as a fraction of the period, and then scaled to an angle


{\displaystyle \varphi }
spanning a whole turn, one gets the phase shift, phase offset, or phase difference of


{\displaystyle G}
relative to


{\displaystyle F}
. If


{\displaystyle F}
is a "canonical" function for a class of signals, like



{\displaystyle \sin(t)}
is for all sinusoidal signals, then


{\displaystyle \varphi }
is called the initial phase of


{\displaystyle G}

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  1. L

    Rearrange formula and work out phase angle

    so far i think Ip = 10 f = 1000hz struggling with the phase angle
  2. Philip551

    How can the direction of propagation help in determining the phase of a wave?

    Using the equation above I know that I have to find parameters k ##\omega## and ##\phi##. $$k = \frac{2\pi}{\lambda}$$ and $$\omega = 2\pi f$$ The problem I've been having is how you would go about finding ##\phi## since by solving: $$y(0,0)=0 \rightarrow sin(\phi)=0 \rightarrow \phi = 0...
  3. nuclearfireball_42

    Can I determine the phase angle of this equation by using the sin function?

    I've got the answer for (a). It's k = 0.78 N/m. I'm having problems with (b). I know that the equation of displacement in this case should either be : x(t) = Asin(ωt + φ) or x(t) = Acos(ωt - φ) where A = amplitudeFrom what I understand, both the equation above should give the same result as...
  4. J

    MHB Amplitude, Period, frequency and phase angle

    HELP! totally lost and confused with this question: A machine is subject to two vibrations at the same time. one vibration has the form: 2cosωt and the other vibration has the form: 3 cos(ωt+0.785). (0.785 is actually expressed as pi/4) determine the resulting vibration and express it in the...
  5. DryRun

    Calculate the phase angle between two sinusoids

    I am trying to do exactly what was stated, by finding it with calculations only, so, without having to draw the curves. Is that possible? Here is my attempt: v1(t) = -10cos(wt + 50) and v2(t) = 12sin(wt-10) v1(t) = -10cos(wt + 50) becomes v1(t) = -10sin(wt+50+90) = v1(t) = -10sin(wt+140) Now...
  6. warhammer

    B Shifting of a Cosine Curve with negative phase angle values

    Continuing on from the summary, the chapter has given a graphed example. We are shown a regular cosine wave with phase angle 0 and another with phase angle (-Pi/4) in order to illustrate that the second curve is shifted rightward to the regular cosine curve because of the negative value. Now, my...
  7. F

    Engineering Draw the magnitude and phase angle of a voltage in this AC circuit

    My solution is attached below. I am not sure if my answer is correct or not , I want to confirm it.
  8. Pierson5

    Complex impedance and phase angle of a circuit

    I've attached my work below. The numbers seem odd to me though. Are my equations correct? Is the phase angle really (0/12)? If so, what are the implications of that?
  9. MedEx

    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.
  10. M

    Coil and resistor in parallel -- How to calculate the phase angle?

    Hello. So I have a coil and a resistor in parallel connection. It is powered by alternating current. I have to calculate angle between voltage and current, what is the formula? I know the reactive resistance in coil, I know resistance of resistor, voltage across both of them and amps flowing...
  11. sneakycooky

    Find the charge q(t) for an LC circuit

    Homework Statement An LC circuit consists of an 82 mH inductor and a 17 microfarad capacitor that initially carries a 180 microC charge. The switch is open for t < 0 and is then closed at t = 0. a. Find the frequency of the resulting oscillations. b. At t = 1 ms, find the charge on the...
  12. Y

    Phase angle and Phase in Simple harmonic motion

    I'm a teacher at a Senior High School in Indonesia. I have two Senior High School physics books (Indonesian book) written about simple harmonic motion formula: y = A sin θ = A sin (ωt + θ0) = A sin 2πφ = A sin 2π (t/T + θ0/2π) phase angle = θ = ωt + θ0 phase of wave = φ = t/T + θ0/2π But I...
  13. K

    I Phase angle of a damped driven harmonic oscillation

    Hello, in every book and on every website (e.g. here http://farside.ph.utexas.edu/teaching/315/Waves/node13.html) i found for driven harmonic osciallation the same solution for phase angle:θ=atan(ωb/(k−mω^2)) where ω is driven freq., m is mass, k is spring constant. I agree with it =it follows...
  14. V

    Relation between power factor and phase angle

    Homework Statement apparently your effective power is V_maxI_max * cos(x) where x is the phase angle. So I must consider only real power Homework Equations power = VI current = I sin(wt) The Attempt at a Solution Let impedence be = e^ix . I'll write current as Ie^i(wt) consideronly the real...
  15. Q

    Using Tektronix Oscilloscope to Measure Phase

    Hi guys, I am working on a project that involves measuring the phase angle between two sinusoidal voltages. The circuit under examination is an RL type (the resistor was in series with the inductor), where the phase of voltage across the inductor is measured relative to the voltage input of the...
  16. Tom Moynihab

    Engineering Voltage and phase between two branches of ac circuit

    【Mod Note: moved from technical forum, so homework template is missing】 In a parallel circuit, one branch contains two equal resistors of resistance ##R_1## connected in series. The other branch contains a resistor of resistance ##R_1## in series with an inductor of variable inductance ##L##...
  17. O

    What is the Phase Angle of an LRC Circuit with Given Components and Frequency?

    Homework Statement A 35 mH inductor with 1.0 resistance is connected in series to a 20 µF capacitor and a 60 Hz, 40-V (rms) source. Calculate the phase angle. Homework Equations tan φ = (XL - XC) / R The Attempt at a Solution Solving for φ: φ = tan -1 [(XL - XC) / R] XL = 2πfL = 13.194 Ω...
  18. G

    A FFT phase result interpretation?

    I have a complex signal eg: cos(wt + phase1) + i*cos(wt + phase2) the frequency of both the waves is same. When i have a look at the phase spectrum of the above signal, i am not able to interpret the phase values. They are making no sense. I tried to determine phase shift for real signals and...
  19. G

    Engineering Current phase angle difference (AC circuit)

    Homework Statement Three receivers, with complex impedance \underline{Z_1}=(125+j375)\Omega,\underline{Z_2}=(700+j100)\Omega,\underline{Z_3}=(500-j500)\Omega, and two sinusoidal current generators of effective values I_{g2}=40mA and unknown I_{g1} are connected. When the switch is open...
  20. O

    Simple Harmonic Motion - Determine quadrant for phase angle.

    Homework Statement When completing this problem I am able to find a value for the phase angle but am unsure of how to find the quadrant for the phase angle therefore unable to get the correct phase angle. Homework Equations Provided in the question: x = xmcos(wt+ phi) The Attempt at a...
  21. J

    Given two waves, find phase angle

    Homework Statement Given two waves characterized by y1(t) = 3 cos wt; y2(t) = 3 sin(wt + 60deg); does y2(t) lead or lag y1(t) and by what phase angle? Homework Equations y1(t) = 3 cos wt; y2(t) = 3 sin(wt + 60deg) The formula I'm given in my book Fundamentals of Applied Electromagnetics is...
  22. snoopies622

    Seeking a phase angle operator for the QHO

    According to Daniel Gillespie in A Quantum Mechanics Primer (1970), " . . . any observable which in classical mechanics is some well behaved function of position and momentum, f(x,p), is represented in quantum mechanics by the operator f ( \hat{x} , \hat {p} ) . That is, a = f (x,p) . . ...
  23. R

    How to compute phase of the signal?

    Suppose you are given a phase spectrum or (/and) equation of the (main) signal only and you are said that the given (main) signal is formed of 3 other signals. Is it possible to compute phases of these three signals from the equation or (/ and) phase spectrum of the (main) signal? Also,what...
  24. dwn

    How to Calculate RLC Phase Angle in Multisim

    Homework Statement This is actually a lab I'm performing on Multisim. I've recreated a circuit that I build in lab class , but I'm not getting the output I need. I am trying to calculate the V and phase angle across each component. I already have the measurements found form the class lab. In...
  25. X

    Finding the phase angle of current through a capacitor?

    Homework Statement Calculate the current in the capacitor shown in the figure below if the voltage input is V(t) = 29cos(377t-30) V, C = 1 micro Farad Homework Equations i = C dv/dt The Attempt at a Solution I essentially differntiate V(t) and multiply by 1 * 10^-6. I then get a negative...
  26. Dustin11H3

    Angle/Coordinate Calculation for two "Pulley" System

    Hello everyone. This is my first post on here. I figured that I would give it a shot. Just as a quick background: I'm studying electrical engineering and I'm working an internship for a machine manufacturing company now. One of the projects I have been assigned is to come up with a system to...
  27. S

    Phase Difference between Voltage and Current

    Homework Statement The circuit above has a 29 resistor and a 11.1 mH inductor. Calculate the theoretical phase difference between the current CPA and voltage VPB if the circuit is driven by a sinusoidal voltage source with a peak amplitude of 3.5 V at the following frequencies: 20 Hz 420 Hz...
  28. D

    Find phase angle of RLC network

    Homework Statement Please see attachment for circuit and parameters. Homework Equations i --> 90 phase angle for inductor so Z of inductor = 0.5<90 sum of voltages = 0 #<40 = #*cos(40) + i*sin(40)*# The Attempt at a Solution shteii01 - 100 + 0.5<90 + V2<theta = 0 --> 100 + 0.5*cos(90) +...
  29. D

    Capacitor needed for phase angle change (RLC network)

    Homework Statement An inductive load is connected to a 120V (rms), 60Hz AC source. The load draws 5.0 kW at a power factor of 0.81 (lagging). You need to improve your power factor to 0.96 (lagging) by adding a capacitor. What is the Capacitance needed (in uF)? Homework Equations P/|S| =...
  30. M

    Impedance and Phase Angle in a Simple Circuit

    Homework Statement Given the circuit above. a) Find I1, I2 and I. b) Find the power used in branch 1 and branch 2. (please correct my "translation" if it's wrong) c) Find the resulting impedance and phase angle. (Is resulting impedance a term?) d) Find the voltage between...
  31. L

    Phase angle between peak source voltage and peak voltage across RLC?

    Homework Statement An LRC series circuit with R = 200Ω , L = 31mH , and C = 1.8μF is powered by an ac voltage source of peak voltage V0 = 540V and frequency f = 550Hz. What are the peak voltages across the inductor, capacitor, and resistor and their phase angles relative to the source...
  32. V

    When getting phase angle difference, do amplitudes have to be positive

    $$f(x)=32sin(x+60°)\quad and\quad g(x)=-1.5sin(x+45°)$$ Would the phase angle difference here be 15° or is that incorrect? I think the amplitudes don't have to be the same but I'm not sure if they at least have to be both positive.
  33. H

    RC circuit question: In vs. Out phase angle

    In an RC circuit, the phase angle between the input and output voltages (not current and voltage) seems to be proportional to the amplitude of the output voltage. That is, as the phase angle between input and output goes to plus or minus 90 degrees, the output voltage goes to 0. Why is that?
  34. E

    Measure Phase Angle: No Oscilloscope Needed

    How can I measure the phase angle between two signals of the same frequency without an oscilloscope? Thanks in advance
  35. T

    Phase Angle between Voltage and Current

    Homework Statement "When only a resistor is connected across the terminals of an ac generator (111 V) that has a fixed frequency, there is a current of 0.465 A in the resistor. When only an inductor is connected across the terminals of this same generator, there is a current of 0.360 A in...
  36. joema

    Origin of phase angle nomenclature?

    It's common to express phase differences between two sinusoidal waveforms as a "phase angle", with a full cycle corresponding to 360 degrees. What is the origin of this nomenclature, and why is phase expressed in degrees? Examined naively, the time domain representation of two waveforms...
  37. W

    AC Circuits Terminology: Phase shift vs Phase Angle

    We talked about AC circuits and phase shifts were discussed. Voltage changes "lag behind" current changes so that's how we get phase shifts. It's like a sinusoid so fine. Then we talked about impedance. There's a real and "imaginary" component to impedance, graphed on x-axis and y-axis...
  38. C

    What does the phase angle phi mean in the harmonic oscillation function?

    The function for simple harmonic oscillation is: Acos(ωT)+\phi Why is there an angle phi added to the function acos(ωT)?
  39. D

    Phase angle between I and V > 90?

    I know that the phase angle between I and V determines the power factor (cos(angle)) and thus the fraction of power supplied that can do real work. Also that a phase angle of 90 degrees means that none of the delivered power can do real work in the system. What happens when the phase angle goes...
  40. S

    How Do You Calculate the Phase Angle in an LCR Circuit?

    Homework Statement A resistor (R), capacitor (C), and inductor (L) are connected in series. What is the complex impedance, Z, of this LCR series combination? An AC supply of voltage V(t)=V0eiωt is applied across an LCR series combination. Derive an expression for the current I(t) in the...
  41. S

    Magnitude and phase angle of the resistor voltage

    the question is to find the magnitude and phase angle of the resistor voltage in the circuit below : http://img513.imageshack.us/img513/1035/ee204.jpg i want you guy's to check my solution please . thanks .
  42. R

    Mystery Circuit Components, Phase Angle, Confirmation and Clarification

    Homework Statement I just did a Signal Processing lab. The manual for the lab is attached, but it was essentially there's a circuit in a box with at most 3 separate linear circuit elements (resistor, capacitor, or inductor) in it. I had to figure out the components without opening it by only...
  43. H

    AC circuit with two components given phase angle

    Homework Statement A circuit contains two elements, but it is not known if they are L, R or C. The current in this circuit when connected to a 1.20×101 V, 60.0 Hz source is 4.70 A and lags the voltage by 4.20×101 degrees. a) What are the two elements? (Answer A,B or C) CL CR LR Homework...
  44. N

    Questions about geometric albedo and phase angle

    If our sun is the source of illumination, how can an object be observed from the Earth at full phase? Wouldn't the Earth eclipse the object? So then why can we see a full moon during full phase? Is it because the moon's orbit is inclined wrt to the Earth-Sun orbit? If so then wouldn't this by...
  45. R

    Calculate phase angle between sine waves?

    Hello, I am trying to work out how to determine the phase angle between two sine wave mathematically? I have setup a Matlab Simulink model and I would like to calculate the phase angle between my current and voltage (both at the same frequency) without using preprogrammed blocks, as i...
  46. D

    How to calculate RMS voltage from triac phase angle

    Hi, In a system that uses a triac to switch mains voltage, how can one calculate the resultant peak voltage, RMS voltage and power for a given phase (conduction) angle e.g. 50°? Many thanks
  47. nukeman

    How do you find the initial phase angle?

    Homework Statement A mass is hanging on a vertical spring, and oscillates in SHM with an amplitude of 10.0 cm, and period 0.500 s. The graph shows its motion as a function of time. At t = 0, the mass is found at x = -7.50 cm below the equilibrium position. Assuming that x(t) = A cos (ωt +...
  48. A

    Phase Angle Explained: What is It?

    Can anyone tell me what is the phase angle and what is the concept behind it?
  49. M

    Finding the phase angle for simple harmonic motion

    Homework Statement A .25 kg block oscillates on the end of a spring with a force constant of 200 N/m. If the oscillation started by elongating the spring 0.15 m and giving the block a speed of 3 m/s, (a) what is the amplitude of the oscillation, and (b) If the clock is started when the block...
  50. Y

    Sinusoidal current phase angle question

    Homework Statement The sinusoidal current i1(t) has a phase angle of 60 degrees. Furthermore, i2(t) attains its positive peak 0.25ms earlier than the current in i2(t) (i.e i1(t) leads i2(t)). Both currents have a frequency of 500 Hz. Determine the phase angle of i2(t) Homework Equations...