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Name Given a frequency of w = 100- rad find the equivalent impedance (Zeg) in Circuit 3. 20 Ω Zeg o 40 Ω U 07 20'n

Name Given a frequency of w = 100- rad find the equivalent impedance (Zeg) in Circuit 3. 20 Ω Zeg o 40 Ω U 07 20'n

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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**Educational Content: Determining Equivalent Impedance in a Circuit** **Problem Statement:** Given a frequency of \(\omega = 100 \, \text{rad/s}\), find the equivalent impedance (\(Z_{eq}\)) in Circuit 3. **Circuit Description:** Circuit 3 consists of a combination of resistors and capacitors. The circuit elements are arranged as follows: 1. **Resistors:** - Three resistors each with a resistance of \(20 \, \Omega\). - One resistor with a resistance of \(40 \, \Omega\). 2. **Capacitors:** - One capacitor with a capacitance of \(10 \, \text{mF}\). - One capacitor with a capacitance of \(5 \, \text{mF}\). **Circuit Layout:** - The three \(20 \, \Omega\) resistors are connected in a combination of series and parallel configurations. - The \(40 \, \Omega\) resistor is connected in parallel with the \(5 \, \text{mF}\) capacitor. - The \(10 \, \text{mF}\) capacitor is connected in series with the parallel combination mentioned above. **Objective:** Determine the equivalent impedance (\(Z_{eq}\)) of the entire circuit, taking into account the given frequency, \(\omega\). **Steps to Solve:** 1. Calculate the impedance of each capacitor using the formula: \[ Z_C = \frac{1}{j\omega C} \] 2. Compute the total impedance of the parallel and series combinations of the resistors and capacitors. 3. Combine these impedances to find the overall equivalent impedance (\(Z_{eq}\)). This exercise provides practice in analyzing circuits with both resistive and capacitive components, enhancing understanding of impedance in AC circuits.
Transcribed Image Text:**Educational Content: Determining Equivalent Impedance in a Circuit** **Problem Statement:** Given a frequency of \(\omega = 100 \, \text{rad/s}\), find the equivalent impedance (\(Z_{eq}\)) in Circuit 3. **Circuit Description:** Circuit 3 consists of a combination of resistors and capacitors. The circuit elements are arranged as follows: 1. **Resistors:** - Three resistors each with a resistance of \(20 \, \Omega\). - One resistor with a resistance of \(40 \, \Omega\). 2. **Capacitors:** - One capacitor with a capacitance of \(10 \, \text{mF}\). - One capacitor with a capacitance of \(5 \, \text{mF}\). **Circuit Layout:** - The three \(20 \, \Omega\) resistors are connected in a combination of series and parallel configurations. - The \(40 \, \Omega\) resistor is connected in parallel with the \(5 \, \text{mF}\) capacitor. - The \(10 \, \text{mF}\) capacitor is connected in series with the parallel combination mentioned above. **Objective:** Determine the equivalent impedance (\(Z_{eq}\)) of the entire circuit, taking into account the given frequency, \(\omega\). **Steps to Solve:** 1. Calculate the impedance of each capacitor using the formula: \[ Z_C = \frac{1}{j\omega C} \] 2. Compute the total impedance of the parallel and series combinations of the resistors and capacitors. 3. Combine these impedances to find the overall equivalent impedance (\(Z_{eq}\)). This exercise provides practice in analyzing circuits with both resistive and capacitive components, enhancing understanding of impedance in AC circuits.
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