hat is the total resistance between node
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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![**Question 8: What is the total resistance between node A and node B?**
**Diagram a:**
- This is a series circuit with two resistors.
- Resistor 1: 4 Ω
- Resistor 2: 2 Ω
- Total resistance in series: \( R_{\text{total}} = 4 \, \Omega + 2 \, \Omega = 6 \, \Omega \)
**Diagram b:**
- This is a parallel circuit with two branches.
- First branch: 0.5 Ω
- Second branch consists of a series circuit:
- Resistor 1: 4 Ω
- Resistor 2: 4 Ω
- Combined series resistance in the second branch: \( 4 \, \Omega + 4 \, \Omega = 8 \, \Omega \)
- Total parallel resistance:
\[
\frac{1}{R_{\text{total}}} = \frac{1}{0.5} + \frac{1}{8}
\]
\[
\frac{1}{R_{\text{total}}} = 2 + 0.125 = 2.125
\]
\[
R_{\text{total}} \approx 0.47 \, \Omega
\]
**Diagram c:**
- This is a series circuit with two resistors.
- Resistor 1: 2 Ω
- Resistor 2: 20 Ω
- Total resistance in series: \( R_{\text{total}} = 2 \, \Omega + 20 \, \Omega = 22 \, \Omega \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6811bcd-02f8-46fa-b044-8f44b9c4930d%2F9d09f3ea-d871-42f1-817d-ca63f77aba0d%2Fyfbu4t3.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 8: What is the total resistance between node A and node B?**
**Diagram a:**
- This is a series circuit with two resistors.
- Resistor 1: 4 Ω
- Resistor 2: 2 Ω
- Total resistance in series: \( R_{\text{total}} = 4 \, \Omega + 2 \, \Omega = 6 \, \Omega \)
**Diagram b:**
- This is a parallel circuit with two branches.
- First branch: 0.5 Ω
- Second branch consists of a series circuit:
- Resistor 1: 4 Ω
- Resistor 2: 4 Ω
- Combined series resistance in the second branch: \( 4 \, \Omega + 4 \, \Omega = 8 \, \Omega \)
- Total parallel resistance:
\[
\frac{1}{R_{\text{total}}} = \frac{1}{0.5} + \frac{1}{8}
\]
\[
\frac{1}{R_{\text{total}}} = 2 + 0.125 = 2.125
\]
\[
R_{\text{total}} \approx 0.47 \, \Omega
\]
**Diagram c:**
- This is a series circuit with two resistors.
- Resistor 1: 2 Ω
- Resistor 2: 20 Ω
- Total resistance in series: \( R_{\text{total}} = 2 \, \Omega + 20 \, \Omega = 22 \, \Omega \)
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