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Determine the current flowing through resistor R given: Ę₁ = 16 V, R₁ = 15 Q, R₂ = 8 N, R₂ = 28 , and R₂ = 12 1 3 4 (Round the FINAL answer to two decimal places.) E₁ R₂ ww R₂

Determine the current flowing through resistor R given: Ę₁ = 16 V, R₁ = 15 Q, R₂ = 8 N, R₂ = 28 , and R₂ = 12 1 3 4 (Round the FINAL answer to two decimal places.) E₁ R₂ 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
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Determine the current flowing through resistor R4

**Problem Statement:** Determine the current flowing through resistor \( R_4 \), given: - \( E_T = 16 \, \text{V} \) (Total voltage) - \( R_1 = 15 \, \Omega \) - \( R_2 = 8 \, \Omega \) - \( R_3 = 28 \, \Omega \) - \( R_4 = 12 \, \Omega \) *(Round the FINAL answer to two decimal places.)* **Circuit Explanation:** The circuit diagram shows: - A voltage source \( E_T = 16 \, \text{V} \) on the left. - Three resistors \( R_1 \), \( R_3 \), and \( R_4 \) connected in series. - Resistor \( R_2 \) connected in parallel to the series combination of \( R_3 \) and \( R_4 \). **Steps for Calculation:** 1. Calculate the equivalent resistance of resistors \( R_3 \) and \( R_4 \) in series: \[ R_{3,4} = R_3 + R_4 = 28 \, \Omega + 12 \, \Omega = 40 \, \Omega \] 2. Calculate the equivalent resistance of the parallel combination of \( R_{3,4} \) and \( R_2 \): \[ \frac{1}{R_{2,3,4}} = \frac{1}{R_2} + \frac{1}{R_{3,4}} = \frac{1}{8 \, \Omega} + \frac{1}{40 \, \Omega} \] \[ \frac{1}{R_{2,3,4}} = \frac{5}{40} + \frac{1}{40} = \frac{6}{40} = \frac{3}{20} \] \[ R_{2,3,4} = \frac{20}{3} \approx 6.67 \, \Omega \] 3. Calculate the total equivalent resistance of the circuit: \[ R_{\text{total}} = R_1 + R_{2,3,4} = 15 \, \Omega + 6.67 \, \Omega
Transcribed Image Text:**Problem Statement:** Determine the current flowing through resistor \( R_4 \), given: - \( E_T = 16 \, \text{V} \) (Total voltage) - \( R_1 = 15 \, \Omega \) - \( R_2 = 8 \, \Omega \) - \( R_3 = 28 \, \Omega \) - \( R_4 = 12 \, \Omega \) *(Round the FINAL answer to two decimal places.)* **Circuit Explanation:** The circuit diagram shows: - A voltage source \( E_T = 16 \, \text{V} \) on the left. - Three resistors \( R_1 \), \( R_3 \), and \( R_4 \) connected in series. - Resistor \( R_2 \) connected in parallel to the series combination of \( R_3 \) and \( R_4 \). **Steps for Calculation:** 1. Calculate the equivalent resistance of resistors \( R_3 \) and \( R_4 \) in series: \[ R_{3,4} = R_3 + R_4 = 28 \, \Omega + 12 \, \Omega = 40 \, \Omega \] 2. Calculate the equivalent resistance of the parallel combination of \( R_{3,4} \) and \( R_2 \): \[ \frac{1}{R_{2,3,4}} = \frac{1}{R_2} + \frac{1}{R_{3,4}} = \frac{1}{8 \, \Omega} + \frac{1}{40 \, \Omega} \] \[ \frac{1}{R_{2,3,4}} = \frac{5}{40} + \frac{1}{40} = \frac{6}{40} = \frac{3}{20} \] \[ R_{2,3,4} = \frac{20}{3} \approx 6.67 \, \Omega \] 3. Calculate the total equivalent resistance of the circuit: \[ R_{\text{total}} = R_1 + R_{2,3,4} = 15 \, \Omega + 6.67 \, \Omega
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