Phasors

In physics, phasor is used to define a complex set of numbers that helps denote the sinusoidal function along with an angular frequency, amplitude, and initial phase. These are also invariant to the time. In simpler terms, the phasors represent the analytic ability that decoy and separate the sinusoid into the product with a complex permanent factor. Another factor that signifies this is the frequency and the time. The constant, not-so-simple products rely on amplitude, including the phase, commonly denoted as the complex amplitude, complex, sinor, and phasor. 

What is phasor? 

Phasor is a scaled line whose length defines the AC quantity that includes the magnitude and the direction from a certain point of time. Meaning phasors are used to depict AC quantities. It involves the displacement and quantity calculated in the clockwise direction. 

A property of the phasor include:

• The maximum value involved in the altering quantity is directly proportional to the length. 

Furthermore, the phasor voltage can differ in the complex amplitude while providing their analytical representation. However, in the linear combination where the functions present in the product are in the linear phase, it contains a similar amount of time or frequency. 

The origin of the term phasor further implies a calculation that is highly equivalent to the vectors and phasors. It can integrate and differentiate the sinusoidal signals into simple algebraic operations. In simple terms, it can allow getting the values by simply calculating the equations. 

Also, if you look at this mathematically, you will notice that the phasor transform is a specific case of the Laplace transform. It can be used to identify the transient response of an RLC circuit. However, you will find it more difficult to apply Laplace transform mathematically. 

What is Phasor Representation? 

The representation of phasor can be understood when the complex number that is functional in a manner of sinusoidal can be represented in the form of phasor voltage. The analytic representation further represents the time-invariant parameters in velocity, phase, and amplitude. 

An assumed constant obtained by guarding the rate of frequency and ensuring the dependence of time is defined as the phasor including complex amplitude. Further, the term phaser is removed from all the calculative fields as these are perpendicular to the vectors. In the 19th century, the phasor voltage and transformation was performed by Charles Proteus Steinmetz.

How can Phasor represent AC? 

Phasor in ac circuit contains a resistor that remains connected with the AC source. In addition, an inductor is also present in the AC source where the capacitor and other joints remain connected with the main source with the help of the capacitor. 

Further, for a resistor, the energy already remains available in the phase, however, in the form of the voltage. In addition, in terms of capacitors, the energy can perform both increments and decrease from the voltage source at a specialised amount. 

The concept of phasor is further used to understand the elevation of the current and the voltage. However, the phasor representation helps to have a clear idea regarding the balanced relationship between the voltage and the current. However, the phasor in the AC circuit is performed in the diagrammatic form. 

What is the Phasor representation in the altering quantities? 

If you assume that the altering voltages and currents work according to the binding of the sine law, then you will have a clear understanding. According to the sine waveform, the generators are made to provide the EMFs. This further provides the easiest form of calculating rotating phasor. 

The sinusoidal quantity can also be obtained with the advantages of these equations for solving various AC problems. Further, the rotating phasor that moves in an anticlockwise direction contains the same velocity. These are also similar to the sinusoidal quantity.

For instance, let’s assume the phasor line or the OA line shows maximum value of emf. Then this value is the altering quantity, or emf, i.e., OA = Emax. 

Also, from this instance, it can be found that the OA is rotating at an angular velocity θ, which is equal to  ‘wt’, here w is the angular velocity and t is the time. The similarity can be found when the EMF passes at a zero magnitude. 

OB= OA sin θ, OB is the stand-out place of the OA present on the Y-axis. 

Where, OB= OA sin θ = Emax sin wt 

However, it is found that the value of the rotating phasor will provide the sinusoidal quantity only in the following situations: 

• When the OA is aligned with the current stage, along with a zero or increasing alternating quantity
• When the length of OA is similar to the maximum value of sinusoidal voltage presented in the relevant scale
• Also, when the angular velocity of OA is in the state of receiving revolution at the time needed for completing one cycle. 

What is Phasor Representation of AC quantities? 

The phasor representation for AC quantities is where the vectors are passed down to find a sinusoidal function. Further, it rotates in an angular motion from the origin. The values representing the vertical component, including the voltage V, can further perform this, and current Ii. Also, in such a situation, the highest value of the current and the voltage is defined by the magnitude of the phasors.

Conclusion 

Thus from the information, it is found that phasor diagrams can provide the sinusoidal AC altering quantities and can be used to represent more than one quantity at a single time. However, depicting alternating quantities by the equations giving instantaneous values of waveforms is challenging. Therefore, to solve ac problems, it’s beneficial to illustrate a sinusoidal quantity by a line of a specific length that rotates in a counterclockwise direction with an angular velocity same as that of the sinusoidal quantity. That rotating line is known as the Phasor. Also, note that the sinusoidal quantity can be voltage or current.