Phase Angle: Formula, Measurement & Phase difference

Phase angle describes the phase shift that exists between overall voltage and total electric current.The voltage triangle matches the phase shift that is there among energetic voltage and general voltage. When it involves the resistance triangle, the phase shift exists between the impedance effective resistance vector. 

Key terms: Phase Angle, Low Phase Angle, phase angle inbody, Phase, Periodic wave, Phase Difference

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What is Phase Angle?

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A wave that repeats as a function of position and time is referred to as Periodic wave. 

Properties of wave:

• Amplitude
• Frequency
• Wavelength
• Speed
• Energy

The phase angle describes the characteristic of a periodic wave. The phase angle is the angular component of a periodic wave. A periodic wave is represented as- Aㄥθ Where, A is the magnitude and Θ is the phase angle.

A phase angle is a characteristic of a periodic wave which tells about the phase shift that is present between total electric current and total voltage. The phase is the location of the waveform at a fraction of time. 

• Phase is expressed in radian and angle. 
• Phase is also the expression of relative displacement among two corresponding features of waveforms having the identical frequency. For example, Zero crossings and Peaks.

Phase Angle

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How is Phase Angle Measured?

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The phase angle plays an important role in instruments where voltage and various sinusoidal waves are involved. In electronics the phase angle refers to the number of lead between the voltage or the number of electronic degrees.

Phase angle is measured using the following steps-

STEP 1. Considering a periodic wave phase angle is measured by the number of units of angular measure between the point of the wave and the reference point. The reference point can be present on another wave or the same waveform.

STEP 2. The reference point must be chosen from the Argand's diagram's real axis to projection of rotating vectors.

STEP 3. Abscissa corresponding to the point on the wave provides us with the phase angle of the point.

• The plotting of the wave takes place on the standard coordinate system. One complete wave cycle has 360° of Phase angle in the Cartesian plot.

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Formula of Phase Angle

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A phase angle refers to the angular component of Periodic wave. It is a complete entity. 

In the figure, where the voltage v1 is passing through the zero cycle before a second voltage v2 leads by 360°/8 or 45°. Phase angle is defined from the fundamental component of each waveform, the distortion of both the signals can give rise to errors, which depends on the nature of distortion. 

Phase angle between voltages v1 and v2

• The majority of modern-day section-measuring gadgets are primarily based on the use of zero-crossing detectors.
•  The time at which every signal crosses the 0-voltage axis is determined, commonly through a squaring-up circuit (for instance, an overdriven amplifier) followed through an excessive-velocity comparator. 
• This produces, in each channel, a cause pulse this is used to power a bistable flip-flop. 
• The output from the bistable is a rectangular wave, the obligation cycle of that's proportional to the phase difference among the input indicators. 
• If this signal is integrated by using a suitable clear out, a dc voltage is produced; this is an analog representation of the segment attitude. 

• This voltage is then displayed on a panel meter (analog or digital) certainly scaled in ranges or radians. 
• Instrumentation using this principle is capable of measuring phase differences to approximately ±0.05° over a huge range of amplitudes and frequencies.

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Phase Difference

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The phase difference refers to the intervals of time by which one wave is ahead or behind of the waveform. Hence, it is a relative property of more than one waveform.

• Phase difference is represented by Greek Letter 'ɸ'. 
• The complete phase is 360 degrees or 2π radians. 
• The phase ahead represents that the wave is ahead of another one having the same frequency.

Phase difference

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Phase Angle Formula and its relation with Phase Difference

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Phase difference Equation of a sine wave using maximum amplitude and voltage is

A(t)  = Amax X sin(ωt ɸ) 

Where, Amax = amplitude of the sine wave

ωt =angular velocity

 and ɸ = the Phase Angle,

So, If ɸ > 0 then the wave has a positive phase of the Phase Angle. Similarly, if ɸ < 0, then the wave has a negative phase of the Phase Angle. 

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Things to Remember

• Phase angle tells us about the phase shift that is present between total electric current and total voltage. 
• Phase is the expression of relative displacement among two features of waveforms having the identical frequency For example, Peaks.
• The phase angle plays an important role in electronics where the voltage and various sinusoidal waves are present. 
• The phase angle is measured using radians or degrees.
• The phase difference refers to the time interval by which one wave is behind or ahead of the waveform. 

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Previous Year's Questions

1. In a fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is ′t′′t′ second. The frequency of vibration of air column is
2. A resonance air column of length 20cm20cm resonates with a tuning fork of frequency 450Hz450Hz. Ignoring the correction, the velocity of sound in air will be​
3. When beats are produced by two progressive waves of the same amplitude and of nearly the same frequency, the ratio of maximum loudness to the loudness of one of the waves will be nn . Where nn is:​…
4. When a stationary wave is formed then its frequency is​…
5. A granite rod of 60cm60cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7×103kg/m32.7×103kg/m3 and its Young's modules is 9.27×1010Pa9.27×1010Pa. What will be the fundamental frequency of the longitudinal vibrations ?​
6. A wave equation which gives the displacement along the direction is given by y=0,001 sin (100r+x)y=0,001 sin (100r+x) where, xx and y are in metre and tt in second. This equation represents a wave​
7. An engine is moving on a circular path of radius 100m100m with a speed of 20m/s20m/s. What will be the frequency observed by an observer standing stationary at the centre of circular path when the engine blows a whistle of frequency 500Hz500Hz?​
8. Two stretched strings have lengths ll and 2l2l while tension are TT and 4T4T respectively. If they are made of same material the ratio of their frequency is….​..
9. Which of the following statements is incorrect for a stationary wave?​
10. Which of the following waves does not travel in vacuum?
11. With propagation of longitudinal waves through a medium, the quantity transmitted is….​.
12. Velocity of sound in vacuum is.,….​.
13. Two waves are represented by the following equation y1−5sin2π(10t−0.1x)y1−5sin2π(10t−0.1x) and v2=10sin2π(10t−0.1x).v2=10sin2π(10t−0.1x). The ratio of intensities I2I1I2I1 will be​
14. The principle of superposition in wave motion tells that in a motion in which two or more waves are simultaneously producing their displacements in a particle then the resultant….​.
15. In stationary waves, nodes are the points where there is…..
16. In an organ pipe of length LL open at both ends, the fundamental mode has a frequency (where vv is a speed of sound in air)​
17. In a stationary wave……
18. In a stationary wave along a string the strain is.….….​..
19. Doppler shift in frequency does not depend upon…...….​..
20. Change in temperature of the medium changes….….​