phase difference and phase shift in an ac circuit

8/16/2019 Phase Difference and Phase Shift in an AC Circuit

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Phase Difference and Phase Shift

hase Difference

the last tutorial, we saw that the Sinusoidal Waveform (http://www.electronics-tutorials.ws/accircuits/sinus

aveform.html) (Sine Wave) can be presented graphically in the time domain along an horizontal zero axis, andne waves have a positive maximum value at time π/2, a negative maximum value at time 3π/2, with zero v

curring along the baseline at 0, π and 2π. However, not all sinusoidal waveforms will pass exactly throug

ro axis point at the same time, but may be “shifted” to the right or to the left of 0 by some value when com

another sine wave.

r example, comparing a voltage waveform to that of a current waveform. This then produces an angular shift or P

fference between the two sinusoidal waveforms. Any sine wave that does not pass through zero at t = 0 has a phase

e phase difference or phase shift as it is also called of a Sinusoidal Waveform (http://amazon.com/dp/1856177

g=basicelecttut-20) is the angle Φ (Greek letter Phi), in degrees or radians that the waveform has shifted from a c

erence point along the horizontal zero axis. In other words phase shift is the lateral difference between two or veforms along a common axis and sinusoidal waveforms of the same frequency can have a phase difference.

e phase difference, Φ of an alternating waveform can vary from between 0 to its maximum time period, T of the wav

ring one complete cycle and this can be anywhere along the horizontal axis between, Φ = 0 to 2π (radians) or Φ

0 depending upon the angular units used.

ase difference can also be expressed as a time shift of τ in seconds representing a fraction of the time period, T for

ample, +10mS or – 50uS but generally it is more common to express phase difference as an angular measurement.

en the equation for the instantaneous value of a sinusoidal voltage or current waveform we developed in the pre

nusoidal Waveform (http://www.electronics-tutorials.ws/accircuits/sinusoidal-waveform.html) will need t

odified to take account of the phase angle of the waveform and this new general expression becomes.

hase Difference Equation

Where:

A - is the amplitude of the waveform.

ωt - is the angular frequency of the waveform in radian/sec.

o

o

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Φ (phi) - is the phase angle in degrees or radians that the waveform has shifted either left or right from t

reference point.

he positive slope of the sinusoidal waveform passes through the horizontal axis “before” t = 0 then the waveform

fted to the left so Φ >0, and the phase angle will be positive in nature, +Φ giving a leading phase angle. In other wo

pears earlier in time than 0 producing an anticlockwise rotation of the vector.

ewise, if the positive slope of the sinusoidal waveform passes through the horizontal x-axis some time “after” t = 0

e waveform has shifted to the right so Φ


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e voltage waveform above starts at zero along the horizontal reference axis, but at that same instant of time the cu

veform is still negative in value and does not cross this reference axis until 30 later. Then there exists a Phase diffe

tween the two waveforms as the current cross the horizontal reference axis reaching its maximum peak and zero v

er the voltage waveform.

the two waveforms are no longer “in-phase”, they must therefore be “out-of-phase” by an amount determined by p

d in our example this is 30 . So we can say that the two waveforms are now 30 out-of phase. The current wavefor

o be said to be “lagging” behind the voltage waveform by the phase angle, Φ. Then in our example above th

veforms have a Lagging Phase Difference so the expression for both the voltage and current above will be given as

here, i lags v by angle Φ

ewise, if the current, i has a positive value and crosses the reference axis reaching its maximum peak and zero valu

me time before the voltage, v then the current waveform will be “leading” the voltage by some phase angle. Then thveforms are said to have a Leading Phase Difference and the expression for both the voltage and the current will b

here, i leads v by angle Φ

e phase angle of a sine wave can be used to describe the relationship of one sine wave to another by using the t

eading” and “Lagging” to indicate the relationship between two sinusoidal waveforms of the same frequency, plotted

e same reference axis. In our example above the two waveforms are out-of-phase by 30 so we can say that i lags

ds i by 30 .

e relationship between the two waveforms and the resulting phase angle can be measured anywhere along the hori

ro axis through which each waveform passes with the “same slope” direction either positive or negative.

AC power circuits this ability to describe the relationship between a voltage and a current sine wave within the

cuit is very important and forms the bases of AC circuit analysis.

he Cosine Waveform

o

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o

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we now know that if a waveform is “shifted” to the right or left of 0 when compared to another sine wave the expre

r this waveform becomes A sin(ωt ± Φ). But if the waveform crosses the horizontal zero axis with a positive going

or π/2 radians before the reference waveform, the waveform is called a Cosine Waveform and the expression bec

osine Expression

e Cosine Wave, simply called “cos”, is as important as the sine wave in electrical engineering. The cosine wave ha

me shape as its sine wave counterpart that is it is a sinusoidal function, but is shifted by +90 or one full quarte

riod ahead of it.

hase Difference between a Sine wave and a Cosine wave

ernatively, we can also say that a sine wave is a cosine wave that has been shifted in the other direction by -90 . Eitheen dealing with sine waves or cosine waves with an angle the following rules will always apply.

ne and Cosine Wave Relationships

hen comparing two sinusoidal waveforms it more common to express their relationship as either a sine or cosine

sitive going amplitudes and this is achieved using the following mathematical identities.

o

mo

o

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using these relationships above we can convert any sinusoidal waveform with or without an angular or phase diffe

m either a sine wave into a cosine wave or vice versa.

the next tutorial about Phasors (http://www.electronics-tutorials.ws/accircuits/phase-difference.html) we will

aphical method of representing or comparing the phase difference between two sinusoids by looking at the p

presentation of a single phase AC quantity along with some phasor algebra relating to the mathematical addition of t

ore phasors.

Sinusoidal Waveforms (http://www.electronics-tutorials.ws/accircuits/sinusoidal-waveform.html) | Phasor Diagrams

Phasor Algebra (http://www.electronics-tutorials.ws/accircuits/phasors.html) »

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RMS Voltage Tutorial (http://www.electronics-tutorials.ws/accircuits/rms-voltage.html)

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Responses to “Phase Difference and Phase Shift”

gs: AC Circuits (http://www.electronics-tutorials.ws/tag/ac-circuits) Phase Difference (http://www.electronics-tutorials.ws/tag/phase-diffe

nusoids (http://www.electronics-tutorials.ws/tag/sinusoids) Waveform (http://www.electronics-tutorials.ws/tag/waveform)

ahmed

thanks

July 4th, 2015 (http://www.electronics-tutorials.ws/accircuits/phase-difference.html/comment-page-1#comment-7277)Reply (http://www.electronics-tutorials.ws/accircuits/phase-difference.html?replytocom=7277#respo

brijesh mishra

reading carefully and think about answer mini some time

December 12th, 2014 (http://www.electronics-tutorials.ws/accircuits/phase-difference.html/comment-page-1#comment-5228)Reply (http://www.electronics-tutorials.ws/accircuits/phase-difference.html?replytocom=5228#respo

sathya

why there is a phase difference between current & voltage,how can it happen?

December 2nd, 2014 (http://www.electronics-tutorials.ws/accircuits/phase-difference.html/comment-page-1#comment-5101)Reply (http://www.electronics-tutorials.ws/accircuits/phase-difference.html?replytocom=5101#respo

nathan MacInnes

The answer to this is simple. I usually teach it to students using a Graphical method, but it is fairly simple to

understand when you look at the Capacitor alone. The Inductor is a little more difficult.

So.

Imagine the Capacitor as an empty container in a closed environment. Now, if I start to pump water (electrons) in to

it (current), it is easy at first, but due to the container being empty, there is no/little pressure present (voltage).

So when Capacitor is empty; V= 0 and I = Max

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This explains the 90 degree phase shift when only a capacitor is used.

note that when the capacitor is Empty, the voltage is 0 and the current is Max, and essentially creates a Short circuit

which is why we cannot create a purely reactive circuits without Purely reactive loads.

January 29th, 2015 (http://www.electronics-tutorials.ws/accircuits/phase-difference.html/comment-page-1#comment-5732)Reply (http://www.electronics-tutorials.ws/accircuits/phase-difference.html?replytocom=5732#respond

Md shahnawazi=sin(wt 180 30)

V=2sin(wt 10)

I lead by phase 200

October 1st, 2014 (http://www.electronics-tutorials.ws/accircuits/phase-difference.html/comment-page-1#comment-2215)Reply (http://www.electronics-tutorials.ws/accircuits/phase-difference.html?replytocom=2215#respo

Sadat Rafi

i=-sin(wt+30)

v=2sin(wt+10)

which one leads?

here answer should be a single one. but it has two answer

v leads i by 160 or, i leads v by 200 degrees .

why?

………..from a book of Robert L Boilestade (USA)

September 30th, 2014 (http://www.electronics-tutorials.ws/accircuits/phase-difference.html/comment-page-1#comment-2201)Reply (http://www.electronics-tutorials.ws/accircuits/phase-difference.html?replytocom=2201#respo

Wayne Storr (http://www.electronics-tutorials.ws)

I can not comment on what other people write in books.

September 30th, 2014 (http://www.electronics-tutorials.ws/accircuits/phase-difference.html/comment-page-1#comment-2202)Reply (http://www.electronics-tutorials.ws/accircuits/phase-difference.html?replytocom=2202#respond

Neeraj Jangid

both answers are correct, it depend on the reference angle, in above problem if u will take reference angle 0 degree

then v lead i by 160 degree and if u will take 180 degree reference angle then i lead v by 200 degree.

December 11th, 2014 (http://www.electronics-tutorials.ws/accircuits/phase-difference.html/comment-page-1#comment-5212)Reply (http://www.electronics-tutorials.ws/accircuits/phase-difference.html?replytocom=5212#respond

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MbiliNE

hmmmm great stuff

March 11th, 2014 (http://www.electronics-tutorials.ws/accircuits/phase-difference.html/comment-page-1#comment-142)Reply (http://www.electronics-tutorials.ws/accircuits/phase-difference.html?replytocom=142#respo

tp://schematics.com/)

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phase difference and phase shift in an ac circuit

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