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,
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?

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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