# 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

G

{\displaystyle G}
.

View More On Wikipedia.org
1. ### Rearrange formula and work out phase angle

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

33. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### Phase Angle Explained: What is It?

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