Question

What is taken as reference for drawing the phasor diagram in series connection?

Answer 1

In a phasor diagram for a series connection, the reference is typically the voltage or current that you choose to represent as a baseline, often taken as the voltage across the first component or the source voltage. The phasors for the other components (like resistors, inductors, and capacitors) are then drawn relative to this reference. The angles of these phasors are determined by their respective impedance characteristics, with the goal of showing the phase relationships between voltage and current in the circuit. Would you like to delve deeper into any specific aspect?

Answer 2

In a series connection of AC circuits, the phasor diagram is a graphical representation that helps visualize the relationships between voltages and currents in the circuit. Here’s how you typically approach drawing the phasor diagram for a series connection:

### 1. **Identify the Components:**
   - **Resistor (R)**
   - **Inductor (L)**
   - **Capacitor (C)**

### 2. **Reference Phasor:**
   - **Current as Reference:** In a series circuit, the same current flows through all components. Therefore, the phasor diagram starts by taking the current as the reference. This phasor is usually drawn along the horizontal axis (real axis) of the diagram. The current phasor is taken as the reference phasor, often represented as a horizontal line.

### 3. **Voltage Across Each Component:**
   - **Resistor (R):** The voltage across the resistor is in phase with the current. Therefore, the voltage phasor for the resistor is drawn in the same direction as the current phasor.
   - **Inductor (L):** The voltage across the inductor leads the current by 90 degrees. In the phasor diagram, this voltage phasor is drawn 90 degrees ahead of the current phasor.
   - **Capacitor (C):** The voltage across the capacitor lags the current by 90 degrees. In the phasor diagram, this voltage phasor is drawn 90 degrees behind the current phasor.

### 4. **Total Voltage Phasor:**
   - To find the total voltage phasor across the entire series circuit, you sum up the individual voltage phasors (resistor, inductor, and capacitor). This involves vector addition of the phasors.

### 5. **Phasor Diagram Steps:**
   - **Step 1:** Draw the current phasor horizontally.
   - **Step 2:** Draw the voltage phasor across the resistor aligned with the current phasor.
   - **Step 3:** Draw the voltage phasor across the inductor leading the current phasor by 90 degrees.
   - **Step 4:** Draw the voltage phasor across the capacitor lagging the current phasor by 90 degrees.
   - **Step 5:** Use vector addition to determine the total voltage phasor. This is usually done by adding the voltage phasors for each component, taking into account their phase relationships.

### Example:

Consider a series RLC circuit:
- If the current is taken as the reference phasor, let’s say it is a horizontal line.
- The resistor voltage phasor is in the same direction as the current.
- The inductor voltage phasor is 90 degrees ahead of the current phasor.
- The capacitor voltage phasor is 90 degrees behind the current phasor.

By placing these phasors correctly, you can visualize how the total voltage across the series circuit relates to the individual voltages and the current.

This method helps in understanding the phase relationships and magnitudes of voltages and currents in AC circuits.