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Determine the voltage dropped on R₂, given: Ę₁ = 225 V, R₁ = 17 º, R₂ = 77 £, and R₂ = 122 (Round the FINAL answer to one decimal place.)

Determine the voltage dropped on R₂, given: Ę₁ = 225 V, R₁ = 17 º, R₂ = 77 £, and R₂ = 122 (Round the FINAL answer to one decimal place.)

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 voltage dropped on R3

To determine the voltage dropped on \( R_3 \), we need to analyze the given circuit and employ Ohm’s Law along with series and parallel circuit rules. **Given:** - Total voltage (\( E_T \)) = 225 V - Resistance \( R_1 \) = 17 Ω - Resistance \( R_2 \) = 77 Ω - Resistance \( R_3 \) = 122 Ω ### Circuit Description: The circuit features a battery (\( E_T \)) providing 225 V. There is a series and parallel combination: - \( R_1 \) is in series with \( R_2 \) and \( R_3 \) which are in parallel with each other. ### Circuit Analysis: 1. **Calculate the equivalent resistance of \( R_2 \) and \( R_3 \) in parallel:** \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R_2} + \frac{1}{R_3} \] \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{77} + \frac{1}{122} \] \[ \frac{1}{R_{\text{parallel}}} = \frac{122 + 77}{77 \times 122} \] \[ R_{\text{parallel}} = \frac{77 \times 122}{199} \] \[ R_{\text{parallel}} \approx 47.1 \, \Omega \] 2. **Determine the total circuit resistance (\( R_T \)):** \[ R_T = R_1 + R_{\text{parallel}} \] \[ R_T = 17 + 47.1 \approx 64.1 \, \Omega \] 3. **Calculate the total current (\( I \)) using Ohm's Law:** \[ I = \frac{E_T}{R_T} \] \[ I = \frac{225}{64.1} \approx 3.5 \, \text{A} \] 4. **Find the voltage drop across \( R_3 \) (\( V_{R3} \)):** Since \( R_2 \) and
Transcribed Image Text:To determine the voltage dropped on \( R_3 \), we need to analyze the given circuit and employ Ohm’s Law along with series and parallel circuit rules. **Given:** - Total voltage (\( E_T \)) = 225 V - Resistance \( R_1 \) = 17 Ω - Resistance \( R_2 \) = 77 Ω - Resistance \( R_3 \) = 122 Ω ### Circuit Description: The circuit features a battery (\( E_T \)) providing 225 V. There is a series and parallel combination: - \( R_1 \) is in series with \( R_2 \) and \( R_3 \) which are in parallel with each other. ### Circuit Analysis: 1. **Calculate the equivalent resistance of \( R_2 \) and \( R_3 \) in parallel:** \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R_2} + \frac{1}{R_3} \] \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{77} + \frac{1}{122} \] \[ \frac{1}{R_{\text{parallel}}} = \frac{122 + 77}{77 \times 122} \] \[ R_{\text{parallel}} = \frac{77 \times 122}{199} \] \[ R_{\text{parallel}} \approx 47.1 \, \Omega \] 2. **Determine the total circuit resistance (\( R_T \)):** \[ R_T = R_1 + R_{\text{parallel}} \] \[ R_T = 17 + 47.1 \approx 64.1 \, \Omega \] 3. **Calculate the total current (\( I \)) using Ohm's Law:** \[ I = \frac{E_T}{R_T} \] \[ I = \frac{225}{64.1} \approx 3.5 \, \text{A} \] 4. **Find the voltage drop across \( R_3 \) (\( V_{R3} \)):** Since \( R_2 \) and
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