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Calculate the impedance Z(jw). At which frequency "w" the voltage of the source vit) and the current i(t) are in phase? (4) es cot at 24 www N() (1) 2H Su 146 0.5 F www

Calculate the impedance Z(jw). At which frequency "w" the voltage of the source vit) and the current i(t) are in phase? (4) es cot at 24 www N() (1) 2H Su 146 0.5 F www

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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IMPEDANCE FIND NETWORK( NEED NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE).

**Problem Statement:** Calculate the impedance \( Z(j\omega) \). At which frequency \( \omega \) the voltage of the source \( V(t) \) and the current \( i(t) \) are in phase? **Diagram Explanation:** The given circuit diagram consists of the following components: 1. An AC voltage source, represented as \( \cos(\omega t) \). 2. A resistor with a resistance of 2 ohms (\( 2\Omega \)). 3. Two inductors in series, with inductances of 2 henrys (\( 2H \)) and 1 henry (\( 1H \)), respectively. 4. A capacitor with a capacitance of 0.5 farads (\( 0.5F \)) in parallel with the 1-henry inductor. The resulting current is denoted as \( i(t) \) and the voltage across the inductor-capacitor parallel combination is \( v(t) \). **Circuit Analysis:** 1. **Series Components:** - Resistor: \( R = 2\Omega \) - Inductors: \( L_1 = 2H \) and \( L_2 = 1H \) 2. **Parallel Combination:** - Inductor: \( L = 1H \) - Capacitor: \( C = 0.5F \) The impedance \( Z(j\omega) \) seen by the source can be found by calculating the impedance of each component and combining them accordingly. - The impedance of an inductor \( L \) at an angular frequency \( \omega \) is \( j\omega L \). - The impedance of a capacitor \( C \) at an angular frequency \( \omega \) is \( \frac{1}{j\omega C} \). Given these definitions, the total impedance can be calculated.
Transcribed Image Text:**Problem Statement:** Calculate the impedance \( Z(j\omega) \). At which frequency \( \omega \) the voltage of the source \( V(t) \) and the current \( i(t) \) are in phase? **Diagram Explanation:** The given circuit diagram consists of the following components: 1. An AC voltage source, represented as \( \cos(\omega t) \). 2. A resistor with a resistance of 2 ohms (\( 2\Omega \)). 3. Two inductors in series, with inductances of 2 henrys (\( 2H \)) and 1 henry (\( 1H \)), respectively. 4. A capacitor with a capacitance of 0.5 farads (\( 0.5F \)) in parallel with the 1-henry inductor. The resulting current is denoted as \( i(t) \) and the voltage across the inductor-capacitor parallel combination is \( v(t) \). **Circuit Analysis:** 1. **Series Components:** - Resistor: \( R = 2\Omega \) - Inductors: \( L_1 = 2H \) and \( L_2 = 1H \) 2. **Parallel Combination:** - Inductor: \( L = 1H \) - Capacitor: \( C = 0.5F \) The impedance \( Z(j\omega) \) seen by the source can be found by calculating the impedance of each component and combining them accordingly. - The impedance of an inductor \( L \) at an angular frequency \( \omega \) is \( j\omega L \). - The impedance of a capacitor \( C \) at an angular frequency \( \omega \) is \( \frac{1}{j\omega C} \). Given these definitions, the total impedance can be calculated.
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