How to Draw a Phasor Diagram for an AC Circuit?

A phasor diagram is a visual representation of the relationships between voltage and current in an AC circuit. It uses vectors to represent the magnitude and phase angle of these quantities.

Understanding Phasors

• Phasors: Phasors are rotating vectors that represent sinusoidal quantities like voltage and current. The length of the phasor represents the magnitude (amplitude) of the quantity, and the angle it makes with the horizontal axis represents its phase angle.
• Phase Angle: The phase angle represents the time difference between the peaks of two sinusoidal waveforms. It's measured in degrees or radians.

Steps to Draw a Phasor Diagram

1. Choose a Reference Axis: Start by drawing a horizontal axis representing the reference for the phase angle. This is usually the voltage across the resistor in the circuit, as it is in phase with the current.
2. Draw the Voltage Phasor: Draw a vector representing the voltage across the resistor. This vector will be along the reference axis.
3. Draw the Current Phasor: Draw a vector representing the current through the resistor. Since the current is in phase with the voltage across the resistor, this vector will also be along the reference axis.
4. Draw Phasors for Other Components: For other components like inductors and capacitors, draw their voltage and current phasors based on their phase relationships:
   • Inductor: The voltage across an inductor leads the current by 90 degrees.
   • Capacitor: The current through a capacitor leads the voltage by 90 degrees.
5. Label the Vectors: Label each vector with the appropriate quantity (e.g., V_R, I_R, V_L, I_L, etc.).
6. Show Phase Angles: Indicate the phase angles between the vectors using appropriate symbols or angles.

Example: RL Circuit

For an RL circuit (resistor and inductor in series), the phasor diagram would look like this:

• V_R: Voltage across the resistor, along the reference axis.
• I: Current through the circuit, also along the reference axis.
• V_L: Voltage across the inductor, leading the current by 90 degrees.
• V_S: Total voltage across the circuit, the vector sum of V_R and V_L.

Practical Insights

• Phasor diagrams are helpful for understanding the phase relationships between voltage and current in AC circuits.
• They help visualize the power factor, which is the cosine of the angle between the voltage and current phasors.
• Phasor diagrams are used in circuit analysis to determine the impedance, which is the total opposition to current flow in an AC circuit.