Representation of AC Current and Voltage by Rotating Vectors - Phasors

Introduction:

In alternating current (AC) circuits, the representation of current and voltage using rotating vectors, also known as phasors, is a crucial concept. Phasors simplify complex AC circuit calculations by converting sinusoidal variations into vectors in the complex plane. This method provides a visual and mathematical way to analyze the phase difference, amplitude, and frequency of AC signals. These notes cover the fundamentals of phasors, their mathematical representation, and practical applications in electrical circuits.



What Are Phasors?

Phasors are rotating vectors used to represent sinusoidal alternating quantities like voltage and current. They simplify AC circuit analysis by providing a graphical representation of amplitude and phase differences.

Characteristics of Phasors:

- Magnitude: Represents the peak value of the sinusoidal quantity.

- Phase Angle: Indicates the phase relationship between different quantities.

- Frequency: Determines the rate of rotation of the phasor.

Mathematical Representation of Phasors:

Phasors are expressed in the complex plane using polar coordinates:

Z = r(cosθ + i sinθ)

where:

- r: Magnitude

- θ: Phase angle

- i: Imaginary unit

Alternatively, they can be written in exponential form as:

Z = re^(iθ)

Representation of AC Voltage and Current Using Phasors:

1. Voltage Representation:

  The voltage waveform V(t) = Vm sin(ωt + φ) is shown as a rotating vector with magnitude Vm and phase φ.

2. Current Representation:

  The current waveform I(t) = Im sin(ωt + ψ) is depicted similarly, with Im as the peak value and ψ as the phase angle.

Read Also: AC Voltage Applied to a Resistor: Class 12 Physics Explained

Phasor Diagram and Its Significance:

A phasor diagram visually represents the phase relationship between current and voltage in AC circuits.

- In Resistive Circuits: Voltage and current are in phase.

- In Inductive Circuits: Current lags behind voltage by 90°.

- In Capacitive Circuits: Current leads voltage by 90°.

Applications of Phasors in AC Circuits:

1. Analysis of RLC circuits.

2. Power factor correction.

3. Calculation of impedance and admittance.

4. Simplification of complex AC networks.

Conclusion:

Phasors are powerful tools in AC circuit analysis, offering both simplicity and precision. They allow engineers and students to visualize and compute the behavior of sinusoidal signals in a straightforward manner. Mastering this concept is essential for understanding advanced topics in Physics and Electrical Engineering, making it a cornerstone of Class 12 Physics studies.