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Find the voltage v R2 15V + + ORI Μ 5 ΚΩ - 10 ΚΩ Μ 03 - 15 ΚΩ + + ο, R2 |

Find the voltage v R2 15V + + ORI Μ 5 ΚΩ - 10 ΚΩ Μ 03 - 15 ΚΩ + + ο, R2 |

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Objective: Find the voltage \( v_{R2} \)** **Diagram Explanation:** The circuit consists of the following components: 1. **Voltage Source:** - A 15 V power source is positioned on the left side of the circuit, providing electrical energy to the circuit. 2. **Resistors:** - There are three resistors in series: - **Resistor \( R1 \):** 5 kΩ - **Resistor \( R2 \):** 15 kΩ - **Resistor \( R3 \):** 10 kΩ 3. **Voltage across Resistors:** - The voltage across the first resistor is labeled as \( v_{R1} \). - The voltage across the second resistor is labeled as \( v_{R2} \), which is the desired voltage to find. - The voltage across the third resistor is labeled as \( v_{R3} \). **Kirchhoff's Voltage Law:** According to Kirchhoff's Voltage Law, the sum of the potential differences (voltages) around any closed loop or mesh is zero. Therefore, the sum of the voltages across the resistors should equal the applied voltage from the source: \[ v_{R1} + v_{R2} + v_{R3} = 15 \, \text{V} \] To find \( v_{R2} \), you can use the voltage division rule since the resistors are in series: \[ v_{R2} = \left(\frac{R2}{R1 + R2 + R3}\right) \times 15 \, \text{V} \] After calculating, this approach will provide the value of \( v_{R2} \).
Transcribed Image Text:**Objective: Find the voltage \( v_{R2} \)** **Diagram Explanation:** The circuit consists of the following components: 1. **Voltage Source:** - A 15 V power source is positioned on the left side of the circuit, providing electrical energy to the circuit. 2. **Resistors:** - There are three resistors in series: - **Resistor \( R1 \):** 5 kΩ - **Resistor \( R2 \):** 15 kΩ - **Resistor \( R3 \):** 10 kΩ 3. **Voltage across Resistors:** - The voltage across the first resistor is labeled as \( v_{R1} \). - The voltage across the second resistor is labeled as \( v_{R2} \), which is the desired voltage to find. - The voltage across the third resistor is labeled as \( v_{R3} \). **Kirchhoff's Voltage Law:** According to Kirchhoff's Voltage Law, the sum of the potential differences (voltages) around any closed loop or mesh is zero. Therefore, the sum of the voltages across the resistors should equal the applied voltage from the source: \[ v_{R1} + v_{R2} + v_{R3} = 15 \, \text{V} \] To find \( v_{R2} \), you can use the voltage division rule since the resistors are in series: \[ v_{R2} = \left(\frac{R2}{R1 + R2 + R3}\right) \times 15 \, \text{V} \] After calculating, this approach will provide the value of \( v_{R2} \).
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