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Determine the total resistance for the circuit, given: R₁ = 152, R₂ = 10 , R₂ = 23 , and R =7Ω (Round the FINAL answer to one decimal place.) R₁ R₂ ww R₂ R₂

Determine the total resistance for the circuit, given: R₁ = 152, R₂ = 10 , R₂ = 23 , and R =7Ω (Round the FINAL answer to one decimal place.) R₁ R₂ ww R₂ 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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Determine the total resistance for the circuit

**Determine the total resistance for the circuit, given:** \( R_1 = 15 \, \Omega, \, R_2 = 10 \, \Omega, \, R_3 = 23 \, \Omega, \) and \( R_4 = 7 \, \Omega \) (Round the FINAL answer to one decimal place.) --- **Circuit Diagram Explanation:** The circuit consists of four resistors and a voltage source \( E_T \). 1. **Series and Parallel Components:** - \( R_1 \) is in series with the combined parallel circuit of resistors \( R_2, R_3, \) and \( R_4 \). - \( R_2 \) is in parallel with \( R_3 \) and \( R_4 \). 2. **Calculating Parallel Resistance:** - The total resistance for the resistors in parallel \( R_T \) can be calculated using the formula: \[ \frac{1}{R_T} = \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} \] - Plugging in the values: \[ \frac{1}{R_T} = \frac{1}{10} + \frac{1}{23} + \frac{1}{7} \] - Calculate \( R_T \) by solving the above equation. 3. **Total Resistance:** - The total resistance \( R_{\text{total}} \) of the circuit is the sum of \( R_1 \) and the calculated parallel resistance \( R_T \): \[ R_{\text{total}} = R_1 + R_T \] 4. **Rounding:** - Round the final answer to one decimal place as instructed. This analysis allows you to understand how different configurations in a circuit can affect the total resistance, which is central to circuit design and analysis.
Transcribed Image Text:**Determine the total resistance for the circuit, given:** \( R_1 = 15 \, \Omega, \, R_2 = 10 \, \Omega, \, R_3 = 23 \, \Omega, \) and \( R_4 = 7 \, \Omega \) (Round the FINAL answer to one decimal place.) --- **Circuit Diagram Explanation:** The circuit consists of four resistors and a voltage source \( E_T \). 1. **Series and Parallel Components:** - \( R_1 \) is in series with the combined parallel circuit of resistors \( R_2, R_3, \) and \( R_4 \). - \( R_2 \) is in parallel with \( R_3 \) and \( R_4 \). 2. **Calculating Parallel Resistance:** - The total resistance for the resistors in parallel \( R_T \) can be calculated using the formula: \[ \frac{1}{R_T} = \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} \] - Plugging in the values: \[ \frac{1}{R_T} = \frac{1}{10} + \frac{1}{23} + \frac{1}{7} \] - Calculate \( R_T \) by solving the above equation. 3. **Total Resistance:** - The total resistance \( R_{\text{total}} \) of the circuit is the sum of \( R_1 \) and the calculated parallel resistance \( R_T \): \[ R_{\text{total}} = R_1 + R_T \] 4. **Rounding:** - Round the final answer to one decimal place as instructed. This analysis allows you to understand how different configurations in a circuit can affect the total resistance, which is central to circuit design and analysis.
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