7. Compute the total resistance between points A a Μ RT RT Μ RT Μ 4Ω 10 Ω 10 ΚΩ 4 Ω (c) 2.2 ΚΩ Μ 10 Ω Μ 4Ω Μ www 2.2 ΚΩ Μ 4Ω 4Ω Μ RT = . 10 ΚΩ ΡτΞ
7. Compute the total resistance between points A a Μ RT RT Μ RT Μ 4Ω 10 Ω 10 ΚΩ 4 Ω (c) 2.2 ΚΩ Μ 10 Ω Μ 4Ω Μ www 2.2 ΚΩ Μ 4Ω 4Ω Μ RT = . 10 ΚΩ ΡτΞ
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![**Problem 7: Compute the Total Resistance Between Points A and B**
**Circuit Diagrams and Resistance Calculations:**
1. **First Circuit:**
- **Components:** Two 4 Ω resistors in series with a 10 Ω resistor in parallel.
- **RT (Total Resistance):**
- The two 4 Ω resistors are in series, so their combined resistance is \(4 Ω + 4 Ω = 8 Ω\).
- This 8 Ω is in parallel with the 10 Ω resistor.
- The total resistance can be calculated using the formula for parallel resistances:
\[
\frac{1}{R_T} = \frac{1}{8 Ω} + \frac{1}{10 Ω}
\]
- Solve for \(R_T\).
2. **Second Circuit:**
- **Components:** A 10 Ω resistor in series with two 4 Ω resistors in parallel.
- **RT (Total Resistance):**
- The two 4 Ω resistors are in parallel, so their combined resistance is:
\[
\frac{1}{R_{parallel}} = \frac{1}{4 Ω} + \frac{1}{4 Ω} = 2 Ω
\]
- This 2 Ω is in series with the 10 Ω resistor.
- The total resistance is \(10 Ω + 2 Ω = 12 Ω\).
3. **Third Circuit:**
- **Components:** Two 10 kΩ resistors and two 2.2 kΩ resistors.
- **RT (Total Resistance):**
- The top 2.2 kΩ is in series with the 10 kΩ resistor, and the bottom 2.2 kΩ is in series with the other 10 kΩ resistor.
- The two resulting series combinations are in parallel.
- Calculate the total resistance:
\[
R_{\text{series 1}} = 2.2 kΩ + 10 kΩ = 12.2 kΩ
\]
\[
R_{\text{series 2}} = 2.2 kΩ + 10 kΩ = 12.2 kΩ
\]
\[
\frac{1}{R_T} = \frac{1}{12.2 kΩ} + \frac{1}{12](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5867f8dc-778e-4b8e-9045-c957ac9725cc%2F7c21e65d-b54f-4069-8d4e-2ec65aa781c1%2Fwrw3qrl_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 7: Compute the Total Resistance Between Points A and B**
**Circuit Diagrams and Resistance Calculations:**
1. **First Circuit:**
- **Components:** Two 4 Ω resistors in series with a 10 Ω resistor in parallel.
- **RT (Total Resistance):**
- The two 4 Ω resistors are in series, so their combined resistance is \(4 Ω + 4 Ω = 8 Ω\).
- This 8 Ω is in parallel with the 10 Ω resistor.
- The total resistance can be calculated using the formula for parallel resistances:
\[
\frac{1}{R_T} = \frac{1}{8 Ω} + \frac{1}{10 Ω}
\]
- Solve for \(R_T\).
2. **Second Circuit:**
- **Components:** A 10 Ω resistor in series with two 4 Ω resistors in parallel.
- **RT (Total Resistance):**
- The two 4 Ω resistors are in parallel, so their combined resistance is:
\[
\frac{1}{R_{parallel}} = \frac{1}{4 Ω} + \frac{1}{4 Ω} = 2 Ω
\]
- This 2 Ω is in series with the 10 Ω resistor.
- The total resistance is \(10 Ω + 2 Ω = 12 Ω\).
3. **Third Circuit:**
- **Components:** Two 10 kΩ resistors and two 2.2 kΩ resistors.
- **RT (Total Resistance):**
- The top 2.2 kΩ is in series with the 10 kΩ resistor, and the bottom 2.2 kΩ is in series with the other 10 kΩ resistor.
- The two resulting series combinations are in parallel.
- Calculate the total resistance:
\[
R_{\text{series 1}} = 2.2 kΩ + 10 kΩ = 12.2 kΩ
\]
\[
R_{\text{series 2}} = 2.2 kΩ + 10 kΩ = 12.2 kΩ
\]
\[
\frac{1}{R_T} = \frac{1}{12.2 kΩ} + \frac{1}{12
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