Representation of AC Current and Voltage by Vector: Definition, Uses, Application & Class 12 Notes

A phasor is a vector quantity that is used to represent the relationship between the current and voltage. In an AC circuit, current and voltage change their magnitude and direction. Instead of showing this change using a sine wave, we represent it by rotating an arrow (vector) called a phasor.

The length of the phasor represents the peak value of voltage or current in the AC circuit. Phasor rotates counterclockwise with an angular velocity (ω) same as the frequency of the AC signal.

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The vertical components of the rotating phasor onto the y-axis are the instantaneous value of the AC signal. The vertical projection traces out a sine wave as the phasor rotates. 

V(t)=Vm sin(ωt+ϕ) 

Where, 

• Vm is peak voltage (length of phasor) 
• ω is the angular frequency (speed of rotation) 
• (ωt+ϕ) angle of phasor 
• ϕ initial angle or phase angle

Phasors are useful in calculating difficult AC circuit problems using algebra rather than calculus. This is useful to calculate the phase relationship in an AC circuit. By identifying phase relationships, a phasor can be visualized geometrically.

Consider an AC circuit with an inductor (L), a capacitor (C), and a resistance (R). 

1. Pure Resistor: V and I are in the same phase. The phasor of voltage and current lies in the same line.
2. Pure Inductor: Current (I) lags voltage by 90°. We draw the current phasor 90° behind the voltage phasor.
3. Pure Capacitor: I leads V by 90°. The current phasor is drawn 90° ahead of the voltage phasor.

Important Links:

Below is the application of phasor representation. 

1. Signal processing
2. Electronics and communication engineering
3. Power calculation in AC systems
4. Electric machines and transformers
5. AC circuit analysis

Students can find here the link for all chapters in Class 12 Physics.

Here we have provided Class 12 Physics NCERT solutions to help students prepare for the exam.