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Determine the total resistance for the circuit, given: R₁ = 102, R₂ = 20, R3 = 10 , and R₁ = 102 (Round the FINAL answer to one decimal place.) ET ww R₁ www

Determine the total resistance for the circuit, given: R₁ = 102, R₂ = 20, R3 = 10 , and R₁ = 102 (Round the FINAL answer to one decimal place.) ET ww R₁ www

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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Determine the total resistance for the circuit 
**Educational Website Content:** --- ### Determining Total Resistance in a Circuit To find the total resistance in the given circuit, use the following values for the resistors: - \( R_1 = 10 \, \Omega \) - \( R_2 = 20 \, \Omega \) - \( R_3 = 10 \, \Omega \) - \( R_4 = 10 \, \Omega \) **Instructions:** Round the final answer to one decimal place. **Circuit Diagram Explanation:** In the schematic: - The power source is indicated as \( E_T \). - Resistor \( R_1 \) is in series with \( R_2 \). - Resistors \( R_3 \) and \( R_4 \) are in parallel with each other, and this parallel combination is in series with the combination of \( R_1 \) and \( R_2 \). **Steps to Calculate Total Resistance:** 1. **Find the equivalent resistance of \( R_3 \) and \( R_4 \) in parallel:** \[ \frac{1}{R_{34}} = \frac{1}{R_3} + \frac{1}{R_4} = \frac{1}{10} + \frac{1}{10} = \frac{2}{10} = \frac{1}{5} \] Therefore, \[ R_{34} = 5 \, \Omega \] 2. **Calculate the total resistance for the entire circuit (\( R_{total} \)):** \[ R_{total} = R_1 + R_2 + R_{34} = 10 + 20 + 5 = 35 \, \Omega \] Thus, the total resistance of the circuit is **35.0 \, \Omega**.
Transcribed Image Text:**Educational Website Content:** --- ### Determining Total Resistance in a Circuit To find the total resistance in the given circuit, use the following values for the resistors: - \( R_1 = 10 \, \Omega \) - \( R_2 = 20 \, \Omega \) - \( R_3 = 10 \, \Omega \) - \( R_4 = 10 \, \Omega \) **Instructions:** Round the final answer to one decimal place. **Circuit Diagram Explanation:** In the schematic: - The power source is indicated as \( E_T \). - Resistor \( R_1 \) is in series with \( R_2 \). - Resistors \( R_3 \) and \( R_4 \) are in parallel with each other, and this parallel combination is in series with the combination of \( R_1 \) and \( R_2 \). **Steps to Calculate Total Resistance:** 1. **Find the equivalent resistance of \( R_3 \) and \( R_4 \) in parallel:** \[ \frac{1}{R_{34}} = \frac{1}{R_3} + \frac{1}{R_4} = \frac{1}{10} + \frac{1}{10} = \frac{2}{10} = \frac{1}{5} \] Therefore, \[ R_{34} = 5 \, \Omega \] 2. **Calculate the total resistance for the entire circuit (\( R_{total} \)):** \[ R_{total} = R_1 + R_2 + R_{34} = 10 + 20 + 5 = 35 \, \Omega \] Thus, the total resistance of the circuit is **35.0 \, \Omega**.
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