For procedures, see your electrical laboratory manual.

Title: Phasor Diagrams


Aim

To demonstrate the validity of using phasors in analyzing simple resistive-reactive circuits.

Apparatus

1. One 2A Variac
2. One 100 Rheostat
3. One Switched capacitor
4. One Inductor
5. One Digital Phase Meter DPM 380
6. One Oscilloscope type D54

Theory

Phasor Diagrams are a graphical way of representing the magnitude and directional relationship between two or more alternating quantities.

Sinusoidal waveforms of the same frequency can have a Phase Difference between themselves which represents the angular difference of the two sinusoidal waveforms. Also, the terms “lead” and “lag”, as well as “in-phase” and “out-of-phase”, are commonly used to indicate the relationship of one waveform to the other.

Basically a rotating vector, simply called a “Phasor” is a scaled line whose length represents an AC quantity that has both magnitude (“peak amplitude”) and direction (“phase”) which is “frozen” at some point in time.

A phasor is a vector that has an arrowhead at one end which signifies partly the maximum value of the vector quantity ( V or I ) and partly the end of the vector that rotates.

Generally, vectors are assumed to pivot at one end around a fixed zero point known as the “point of origin” while the arrowed end representing the quantity, freely rotates in an anti-clockwise direction at an angular velocity, ( ω ) of one full revolution for every cycle. This anti-clockwise rotation of the vector is considered to be a positive rotation. Likewise, a clockwise rotation is considered to be a negative rotation.

The phase of an alternating quantity at any instant in time can be represented by a phasor diagram, so phasor diagrams can be thought of as “functions of time”. A complete sine wave can be constructed by a single vector rotating at an angular velocity of ω = 2πƒ, where Æ’ is the frequency of the waveform. Then a Phasor is a quantity that has both “Magnitude” and “Direction”.

Generally, when constructing a phasor diagram, the angular velocity of a sine wave is always assumed to be: ω in rad/sec.

In the context of phasors, phase angle refers to the angular component of the complex number representation of the function. The phase angle is the phase difference between the voltage applied to the impedance and the current driven through it.

Phase Difference is used to describe the difference in degrees or radians when two or more alternating quantities reach their maximum or zero values.

The phase difference or phase shift as it is also called a Sinusoidal Waveform is the angle Φ (Greek letter Phi), in degrees or radians that the waveform has shifted from a certain reference point along the horizontal zero axes. In other words, the phase shift is the lateral difference between two or more waveforms along a common axis and sinusoidal waveforms of the same frequency can have a phase difference.

The phase difference can also be expressed as a time shift of Ï„ in seconds representing a fraction of the time period.