Three resistors with resistances R¡ = 49.0 Q, R2 = 23.0 Q, and R3 = 91.0 2 are placed along the sides of a triangle as shown in circuit 1. What are the values of the resistances Ra, Rp, and Re that would provide an equivalent circuit as arranged in circuit 2? ww R,

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Three resistors with resistances ?1=49.0R1=49.0 Ω, ?2=23.0R2=23.0 Ω, and ?3=91.0R3=91.0 Ω are placed along the sides of a triangle as shown in circuit 1. What are the values of the resistances ?aRa , ?bRb , and ?cRc that would provide an equivalent circuit as arranged in circuit 2?

# Problem Statement: Calculation of Equivalent Resistances in Delta-Wye Transformation

**Introduction:**
Three resistors with resistances \( R_1 = 49.0 \Omega \), \( R_2 = 23.0 \Omega \), and \( R_3 = 91.0 \Omega \) are arranged along the sides of a triangle as shown in Circuit 1. The objective is to calculate the values of the resistances \( R_a \), \( R_b \), and \( R_c \) that would provide an equivalent circuit as arranged in Circuit 2.

**Problem Setup:**
- **Given Resistors in Delta Configuration (Circuit 1):**
  - \( R_1 = 49.0 \Omega \)
  - \( R_2 = 23.0 \Omega \)
  - \( R_3 = 91.0 \Omega \)

- **Required:**
  Calculate the equivalent resistances \( R_a \), \( R_b \), and \( R_c \) for the Wye (Star) Configuration (Circuit 2).

**Equations for Delta to Wye Transformation:**
1. \( R_a = \frac{R_1 R_2}{R_1 + R_2 + R_3} \)
2. \( R_b = \frac{R_2 R_3}{R_1 + R_2 + R_3} \)
3. \( R_c = \frac{R_3 R_1}{R_1 + R_2 + R_3} \)

**Diagrams:**

- **Circuit 1: Delta Configuration**
  There's a triangle with vertices marked as A, B, and C. Resistor \( R_1 \) is between vertices B and A, \( R_2 \) is between vertices B and C, and \( R_3 \) is between vertices A and C.

- **Circuit 2: Wye Configuration**
  The vertices A, B, and C are the same; however, three resistors \( R_a \), \( R_b \), and \( R_c \) are connected such that:
  - Resistor \( R_a \) is between vertex A and a central node,
  - Resistor \( R_b \) is between vertex B and the central node,
  - Resistor \( R_c \) is between vertex C and the central node.

**
Transcribed Image Text:# Problem Statement: Calculation of Equivalent Resistances in Delta-Wye Transformation **Introduction:** Three resistors with resistances \( R_1 = 49.0 \Omega \), \( R_2 = 23.0 \Omega \), and \( R_3 = 91.0 \Omega \) are arranged along the sides of a triangle as shown in Circuit 1. The objective is to calculate the values of the resistances \( R_a \), \( R_b \), and \( R_c \) that would provide an equivalent circuit as arranged in Circuit 2. **Problem Setup:** - **Given Resistors in Delta Configuration (Circuit 1):** - \( R_1 = 49.0 \Omega \) - \( R_2 = 23.0 \Omega \) - \( R_3 = 91.0 \Omega \) - **Required:** Calculate the equivalent resistances \( R_a \), \( R_b \), and \( R_c \) for the Wye (Star) Configuration (Circuit 2). **Equations for Delta to Wye Transformation:** 1. \( R_a = \frac{R_1 R_2}{R_1 + R_2 + R_3} \) 2. \( R_b = \frac{R_2 R_3}{R_1 + R_2 + R_3} \) 3. \( R_c = \frac{R_3 R_1}{R_1 + R_2 + R_3} \) **Diagrams:** - **Circuit 1: Delta Configuration** There's a triangle with vertices marked as A, B, and C. Resistor \( R_1 \) is between vertices B and A, \( R_2 \) is between vertices B and C, and \( R_3 \) is between vertices A and C. - **Circuit 2: Wye Configuration** The vertices A, B, and C are the same; however, three resistors \( R_a \), \( R_b \), and \( R_c \) are connected such that: - Resistor \( R_a \) is between vertex A and a central node, - Resistor \( R_b \) is between vertex B and the central node, - Resistor \( R_c \) is between vertex C and the central node. **
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