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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)
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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**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
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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