Phasor Representation AC: Current and Voltage

Phasor Representation AC is a rotating vector which is a scaled line whose length reflects an AC quantity with both magnitude (peak amplitude) and direction (phase) that is "frozen" at a specific point in time.

• The arrowed end indicates the quantity freely rotates in an anti-clockwise direction at an angular velocity (ω), while vectors are considered to pivot at one end around a fixed zero point known as the "point of origin".
• The angular velocity of a sine wave is always assumed to be in rad/sec when generating a phasor diagram.
• A phasor representation is represented as a complex number which functions in a sinusoidal manner.
• In our homes and offices, the electric mains supply is a voltage that varies in time like a sine function.

Key Terms: Phasor, Phasor representation, AC Current, Voltage, Angular velocity, Waves, Velocity, Waveform, Current, Emf

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Phasor Representation of AC and Voltage

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Assume that alternating voltages and currents obey the sine law and that generators are built to produce sine waveform EMFs.

• The above-mentioned assumption simplifies the calculations.
• It's inconvenient to represent alternating quantities with a waveform or equations that give immediate values.
• It is preferable to depict a sinusoidal quantity (voltage or current) by a line of fixed length moving in a counterclockwise direction with the same angular velocity as the sinusoidal quantity while solving ac issues.
• The phasor is a rotating line like this.

Phasor Representation of AC and Voltage

Consider the line OA (or phasor), which represents to scale of the maximum value of an alternating quantity, say emf, i.e., OA = Emax and rotates counter-clockwise at an angular velocity of radians/second around the point O.

• When two or more phasors happen to overlap, an arrowhead is placed at the outer end of the phasor, partly to indicate which end is expected to move and partly to indicate the precise length of the phasor.
• When it has rotated via an angle of t from the position it was in when the emf was at zero.
• The value of the emf at that instant

OB = OA sinθ = E_max sin ωt = e

Where OB is the projection of OA on the Y-Axis.

In mathematical form, there are three ways to represent phasors:

1. Polar Form: Assume we have a phasor with an amplitude of Vm and a polar form that makes an angle with the horizontal axis. As a result, we can write it as Vm in the polar form.
2. Rectangular Form: In Rectangular Form, any phasor can be shown as a complex number, such as A+iB.
3. Exponential Form: In this case, the phasor is represented as V_me^jΦ

The video below explains this:

Representation of AC by Rotating Phasors Detailed Video Explanation:

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Advantages of Phasor Representation

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The phasor representation ac can be used to perform mathematical operations such as addition, multiplication, and division. Any common values, such as RMS, peak values, phase angles, and so on, can be used in the calculation.

• The objective of a phasor diagram is to illustrate the steady-state inter-relationship between quantities that change sinusoidally in time in a pictorial fashion.
• We envision all phasors turning counterclockwise at a consistent pace, completing one revolution per supply cycle.
• Phasors are a valuable tool for visualizing what's happening in an AC circuit (and in fact for many situations involving sinusoidal waves).
• They're also handy for thinking about phase shifts between sinusoidal values.
• The phase relationship between alternating current and alternating e.m.f. is represented by a Phasor Representation ac.
• The peak values are represented by phasors, which can be turned in an anticlockwise direction to represent them.
• In physics and engineering, a phase vector or phasor is a sine wave whose amplitude and frequency are time-varying.
• Phasors divide the behavior of a sinusoid into three distinct factors: phase information, frequency, and amplitude

Advantages of Phasor Representation

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Difference between Phasor and Vector

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Phasors are really vectors that represent a certain concept. Vectors can be used to represent anything with magnitude and direction in any number of dimensions in a variety of circumstances.

• Although vectors can be used for the same things as phasors can, the word 'phase' in 'phase-vector' or 'phasor' implies certain information.
• A sinusoid is represented by a phase vector, which implies a frequency of rotation about the origin point.
• As a result, a single phasor has an assumed circular location. 

Difference between Phasor and Vector

The angle's significance is measured in relation to other phasors in the same diagram, and the traditional reference is the positive horizontal x-axis on a standard graph.

• From that line, phase angles are measured in an anti-clockwise orientation.
• The Argand plane, which permits complex numbers, is where a phasor is drawn.
• As a result, any point in the Argand plane can represent a phasor in one of the following ways.
• The benefit of encoding so much data in the phasor is that it simplifies potentially complex calculations into simple vector additions.

For Example:

R + j X = The real component is R, whereas the imaginary component is X.

|Z|eja, where an is the phase angle (radians) and Z is the vector's magnitude.

Where w = 2 pi f, A(cos(wt) + j sin(wt)

f stands for frequency.

A is for amplitude.

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How Does a Capacitor Work in an AC Circuit?

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The capacitor plates in an alternating current circuit continue to charge and discharge due to the periodic change of direction and pulsing value of the electric current and then get charged with opposite polarity and discharged again, thus continuing the cycle.

• Alternating currents reverse direction on a regular basis, causing the polarity of capacitor plates to shift.
• It is constantly charged and discharged. It returns back the electrical energy it had stored while being discharged, hence an ideal capacitive circuit consumes no power. 
• When a capacitor is linked in series with a functioning circuit, it charges to the maximum alternating voltage.
• During the period when the source voltage drops to zero and then rises in the opposite direction, the capacitor discharges and gives power to the working circuit, maintaining the magnitude of voltage to the appliance connected in parallel with it constantly.

How Does a Capacitor Work in an AC Circuit

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Things To Remember

• For visualizing sinusoidally time-variant quantities, phasors are quite useful. 
• Phasors can help us visualize the phase difference between current and voltage in addition to visualizing AC current and voltage.
• A phasor representation is represented as a complex number which functions in a sinusoidal manner.
• A phasor is a spinning vector with a length equal to the highest value of a sinusoidally varying physical quantity and an angular speed numerically equal to the sinusoidally varying function's angular frequency.
• Phasors also assist in the solution of some circuit issues, such as the addition of phase-discriminated voltages.
• Vectors can be used to represent anything with magnitude and direction in any number of dimensions in a variety of circumstances.

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