What is taken as reference for drawing the phasor diagram in parallel connection?
2 Answers
In electrical engineering, when drawing phasor diagrams for parallel connections, the following principles and references are typically used:
### Reference for Drawing Phasor Diagrams in Parallel Connection
1. **Reference Phasor:**
- **Voltage Phasor:** In a parallel AC circuit, all components share the same voltage across them. Therefore, the voltage phasor is often used as the reference. This phasor is usually represented horizontally on the diagram (typically along the real axis), and all other phasors (current phasors) are drawn relative to this reference phasor.
2. **Phasor Diagram Steps:**
- **Step 1: Draw the Reference Voltage Phasor:**
- Start by drawing the voltage phasor as a horizontal line. This phasor represents the voltage across all parallel components and is taken as the reference phasor (0° or 0 radians).
- **Step 2: Determine the Current Phasors:**
- For each parallel branch, calculate the current phasor based on the impedance of that branch and the voltage. Use Ohm’s law, \( I = \frac{V}{Z} \), where \( V \) is the reference voltage phasor, and \( Z \) is the impedance of the branch.
- Represent each current phasor relative to the reference voltage phasor. The angle between the current phasor and the reference voltage phasor depends on the impedance's phase angle (e.g., resistive, capacitive, or inductive).
- **Step 3: Add Phasors Together (If Required):**
- If you need to find the total current or total impedance of the parallel circuit, add the individual current phasors (vectorially) to get the total current phasor. For the total impedance, use the formula for combining parallel impedances.
### Key Points to Remember:
- **All voltages in parallel circuits are the same**, so the voltage phasor is the same for each branch and serves as the reference.
- **Currents in parallel circuits are different** and vary based on the branch impedance, so current phasors need to be drawn with respect to the voltage reference.
By using the voltage phasor as a reference, you simplify the process of analyzing and combining the effects of different branches in parallel circuits.
### Reference for Drawing Phasor Diagrams in Parallel Connection
1. **Reference Phasor:**
- **Voltage Phasor:** In a parallel AC circuit, all components share the same voltage across them. Therefore, the voltage phasor is often used as the reference. This phasor is usually represented horizontally on the diagram (typically along the real axis), and all other phasors (current phasors) are drawn relative to this reference phasor.
2. **Phasor Diagram Steps:**
- **Step 1: Draw the Reference Voltage Phasor:**
- Start by drawing the voltage phasor as a horizontal line. This phasor represents the voltage across all parallel components and is taken as the reference phasor (0° or 0 radians).
- **Step 2: Determine the Current Phasors:**
- For each parallel branch, calculate the current phasor based on the impedance of that branch and the voltage. Use Ohm’s law, \( I = \frac{V}{Z} \), where \( V \) is the reference voltage phasor, and \( Z \) is the impedance of the branch.
- Represent each current phasor relative to the reference voltage phasor. The angle between the current phasor and the reference voltage phasor depends on the impedance's phase angle (e.g., resistive, capacitive, or inductive).
- **Step 3: Add Phasors Together (If Required):**
- If you need to find the total current or total impedance of the parallel circuit, add the individual current phasors (vectorially) to get the total current phasor. For the total impedance, use the formula for combining parallel impedances.
### Key Points to Remember:
- **All voltages in parallel circuits are the same**, so the voltage phasor is the same for each branch and serves as the reference.
- **Currents in parallel circuits are different** and vary based on the branch impedance, so current phasors need to be drawn with respect to the voltage reference.
By using the voltage phasor as a reference, you simplify the process of analyzing and combining the effects of different branches in parallel circuits.
In electrical engineering, the phasor diagram for a parallel connection of AC circuits is a graphical representation that shows the phase relationships between different voltages and currents in the system. Here’s a detailed explanation of how to draw and interpret these diagrams, focusing on the reference used:
### **1. **Reference for the Phasor Diagram**:
#### **Reference Voltage**:
- **Common Practice**: In most phasor diagrams, the voltage across the parallel elements is used as the reference. This is because, in a parallel circuit, all components share the same voltage. This voltage is usually chosen as the reference phasor and is represented as a horizontal line or vector.
- **Reference Choice**: The reference voltage is typically set at a phase angle of 0 degrees for simplicity, meaning it is drawn along the positive real axis in the phasor diagram. This makes it easier to compare the phase angles of currents or other voltages relative to this reference.
### **2. **Steps to Draw the Phasor Diagram**:
#### **Step 1: Draw the Reference Voltage**:
- **Draw a horizontal line** to represent the reference voltage phasor. This line is usually labeled with the magnitude of the voltage and is positioned along the positive x-axis. The angle of this phasor is considered to be 0 degrees.
#### **Step 2: Draw the Voltage Phasors Across Each Component**:
- **In a parallel circuit**, each component (resistor, capacitor, inductor) has the same voltage across it. Therefore, if you need to represent the voltage phasors across different components or loads, they will all align with the reference voltage phasor. For clarity, it is usually enough to show just the reference voltage.
#### **Step 3: Draw the Current Phasors**:
- **For each component**, draw the current phasor based on the impedance and its phase relationship with the reference voltage:
- **Resistor**: The current phasor will be in phase with the voltage phasor.
- **Capacitor**: The current phasor will lead the voltage phasor by 90 degrees.
- **Inductor**: The current phasor will lag the voltage phasor by 90 degrees.
### **3. **Interpreting the Phasor Diagram**:
#### **Currents and Voltages**:
- **Magnitude and Phase**: The lengths of the phasors represent the magnitudes of the currents or voltages, and the angles represent the phase differences.
- **Vector Addition**: In a parallel circuit, the total current is the sum of the individual currents. This is represented by vector addition of the current phasors. For resistors, capacitors, and inductors, you sum their respective phasors to get the total current phasor.
#### **Total Current Phasor**:
- **Sum of Phasors**: The total current phasor can be found by vectorially adding all the individual current phasors. This provides insight into the total current flowing from the source into the parallel network.
### **Example Phasor Diagram**:
Imagine you have a parallel circuit with a resistor, an inductor, and a capacitor connected to a sinusoidal voltage source:
1. **Reference Voltage Phasor**: Draw a horizontal line to represent the voltage across the parallel components.
2. **Resistor Current Phasor**: Draw this in phase with the reference voltage.
3. **Capacitor Current Phasor**: Draw this phasor leading the reference voltage phasor by 90 degrees.
4. **Inductor Current Phasor**: Draw this phasor lagging the reference voltage phasor by 90 degrees.
### **Summary**:
In a parallel AC circuit, the reference for drawing the phasor diagram is usually the voltage across the parallel components. All components share the same voltage, so it is set as the zero-degree reference phasor. Currents through individual components are drawn relative to this reference voltage, reflecting their phase relationships and magnitudes.
This method provides a clear visual understanding of how different components in the parallel circuit interact and how the total current is affected by the phase relationships of the individual currents.
### **1. **Reference for the Phasor Diagram**:
#### **Reference Voltage**:
- **Common Practice**: In most phasor diagrams, the voltage across the parallel elements is used as the reference. This is because, in a parallel circuit, all components share the same voltage. This voltage is usually chosen as the reference phasor and is represented as a horizontal line or vector.
- **Reference Choice**: The reference voltage is typically set at a phase angle of 0 degrees for simplicity, meaning it is drawn along the positive real axis in the phasor diagram. This makes it easier to compare the phase angles of currents or other voltages relative to this reference.
### **2. **Steps to Draw the Phasor Diagram**:
#### **Step 1: Draw the Reference Voltage**:
- **Draw a horizontal line** to represent the reference voltage phasor. This line is usually labeled with the magnitude of the voltage and is positioned along the positive x-axis. The angle of this phasor is considered to be 0 degrees.
#### **Step 2: Draw the Voltage Phasors Across Each Component**:
- **In a parallel circuit**, each component (resistor, capacitor, inductor) has the same voltage across it. Therefore, if you need to represent the voltage phasors across different components or loads, they will all align with the reference voltage phasor. For clarity, it is usually enough to show just the reference voltage.
#### **Step 3: Draw the Current Phasors**:
- **For each component**, draw the current phasor based on the impedance and its phase relationship with the reference voltage:
- **Resistor**: The current phasor will be in phase with the voltage phasor.
- **Capacitor**: The current phasor will lead the voltage phasor by 90 degrees.
- **Inductor**: The current phasor will lag the voltage phasor by 90 degrees.
### **3. **Interpreting the Phasor Diagram**:
#### **Currents and Voltages**:
- **Magnitude and Phase**: The lengths of the phasors represent the magnitudes of the currents or voltages, and the angles represent the phase differences.
- **Vector Addition**: In a parallel circuit, the total current is the sum of the individual currents. This is represented by vector addition of the current phasors. For resistors, capacitors, and inductors, you sum their respective phasors to get the total current phasor.
#### **Total Current Phasor**:
- **Sum of Phasors**: The total current phasor can be found by vectorially adding all the individual current phasors. This provides insight into the total current flowing from the source into the parallel network.
### **Example Phasor Diagram**:
Imagine you have a parallel circuit with a resistor, an inductor, and a capacitor connected to a sinusoidal voltage source:
1. **Reference Voltage Phasor**: Draw a horizontal line to represent the voltage across the parallel components.
2. **Resistor Current Phasor**: Draw this in phase with the reference voltage.
3. **Capacitor Current Phasor**: Draw this phasor leading the reference voltage phasor by 90 degrees.
4. **Inductor Current Phasor**: Draw this phasor lagging the reference voltage phasor by 90 degrees.
### **Summary**:
In a parallel AC circuit, the reference for drawing the phasor diagram is usually the voltage across the parallel components. All components share the same voltage, so it is set as the zero-degree reference phasor. Currents through individual components are drawn relative to this reference voltage, reflecting their phase relationships and magnitudes.
This method provides a clear visual understanding of how different components in the parallel circuit interact and how the total current is affected by the phase relationships of the individual currents.