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)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35b78b40-6a45-4b58-8186-5bcc6d82334d%2F5f0e02f5-751a-47af-9b4d-068f4c0370d3%2F57ov10o_processed.png&w=3840&q=75)
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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