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Determine the total resistance for the circuit, given: R₂₁ = 100, R₂ = 50, R₂ = 14 Q, and R₂ = 150 (Round the FINAL answer to one decimal place.) +||| E₁ www R₁ ww R₂

Determine the total resistance for the circuit, given: R₂₁ = 100, R₂ = 50, R₂ = 14 Q, and R₂ = 150 (Round the FINAL answer to one decimal place.) +||| E₁ www R₁ ww 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** Given: - \( R_1 = 10 \, \Omega \) - \( R_2 = 5 \, \Omega \) - \( R_3 = 14 \, \Omega \) - \( R_4 = 15 \, \Omega \) (Round the FINAL answer to one decimal place.) **Circuit Diagram Explanation:** The circuit diagram consists of four resistors and a voltage source labeled \( E_T \). The resistors \( R_1 \), \( R_2 \), \( R_3 \), and \( R_4 \) are arranged in a combination of series and parallel configurations. - **Series Components:** - Resistor \( R_1 \) is in series with the parallel combination of \( R_2 \), \( R_3 \) and \( R_4 \). - **Parallel Components:** - Resistors \( R_2 \), \( R_3 \), and \( R_4 \) are connected in parallel to each other. **Steps to Calculate Total Resistance:** 1. **Calculate the Equivalent Resistance of the Parallel Resistors:** \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} \] Substituting the given values: \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{5} + \frac{1}{14} + \frac{1}{15} \] \[ R_{\text{parallel}} = \left(\frac{1}{5} + \frac{1}{14} + \frac{1}{15}\right)^{-1} \] 2. **Calculate the Total Resistance in the Circuit:** \[ R_{\text{total}} = R_1 + R_{\text{parallel}} \] 3. **Round the Final Answer to One Decimal Place.**
Transcribed Image Text:**Determine the Total Resistance for the Circuit** Given: - \( R_1 = 10 \, \Omega \) - \( R_2 = 5 \, \Omega \) - \( R_3 = 14 \, \Omega \) - \( R_4 = 15 \, \Omega \) (Round the FINAL answer to one decimal place.) **Circuit Diagram Explanation:** The circuit diagram consists of four resistors and a voltage source labeled \( E_T \). The resistors \( R_1 \), \( R_2 \), \( R_3 \), and \( R_4 \) are arranged in a combination of series and parallel configurations. - **Series Components:** - Resistor \( R_1 \) is in series with the parallel combination of \( R_2 \), \( R_3 \) and \( R_4 \). - **Parallel Components:** - Resistors \( R_2 \), \( R_3 \), and \( R_4 \) are connected in parallel to each other. **Steps to Calculate Total Resistance:** 1. **Calculate the Equivalent Resistance of the Parallel Resistors:** \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} \] Substituting the given values: \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{5} + \frac{1}{14} + \frac{1}{15} \] \[ R_{\text{parallel}} = \left(\frac{1}{5} + \frac{1}{14} + \frac{1}{15}\right)^{-1} \] 2. **Calculate the Total Resistance in the Circuit:** \[ R_{\text{total}} = R_1 + R_{\text{parallel}} \] 3. **Round the Final Answer to One Decimal Place.**
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