What is Phase angle: Definition and 83 Discussions
In physics and mathematics, the phase of a periodic function
F
{\displaystyle F}
of some real variable
t
{\displaystyle t}
(such as time) is an angle-like quantity representing the fraction of the cycle covered up to
t
{\displaystyle t}
. It is denoted
ϕ
(
t
)
{\displaystyle \phi (t)}
and expressed in such a scale that it varies by one full turn as the variable
t
{\displaystyle t}
goes through each period (and
F
(
t
)
{\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
2
π
{\displaystyle 2\pi }
as the variable
t
{\displaystyle t}
completes a full period.This convention is especially appropriate for a sinusoidal function, since its value at any argument
t
{\displaystyle t}
then can be expressed as the sine of the phase
ϕ
(
t
)
{\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
ϕ
(
t
)
{\displaystyle \phi (t)}
is also a periodic function, with the same period as
F
{\displaystyle F}
, that repeatedly scans the same range of angles as
t
{\displaystyle t}
goes through each period. Then,
F
{\displaystyle F}
is said to be "at the same phase" at two argument values
t
1
{\displaystyle t_{1}}
and
t
2
{\displaystyle t_{2}}
(that is,
ϕ
(
t
1
)
=
ϕ
(
t
2
)
{\displaystyle \phi (t_{1})=\phi (t_{2})}
) if the difference between them is a whole number of periods.
The numeric value of the phase
ϕ
(
t
)
{\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
F
{\displaystyle F}
with a shifted version
G
{\displaystyle G}
of it. If the shift in
t
{\displaystyle t}
is expressed as a fraction of the period, and then scaled to an angle
φ
{\displaystyle \varphi }
spanning a whole turn, one gets the phase shift, phase offset, or phase difference of
G
{\displaystyle G}
relative to
F
{\displaystyle F}
. If
F
{\displaystyle F}
is a "canonical" function for a class of signals, like
sin
(
t
)
{\displaystyle \sin(t)}
is for all sinusoidal signals, then
φ
{\displaystyle \varphi }
is called the initial phase of
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...
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...
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...
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...
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...
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?
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. 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...
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...
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...
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...
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...
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...
【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##...
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...
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...
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...
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...
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...
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) . . ...
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...
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...
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...
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...
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...
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) +...
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| =...
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...
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...
$$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.
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?
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...
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...
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...
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...
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...
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 .
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...
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...
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...
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...
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
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 +...
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...
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...