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3. Use Phasors analysis to calculate the following for this single phase, AC steady-state circuit: • a. Z1, Z2, and Z3 as complex impedances in Ohms b. The parallel combination Z2//Z3 c. Zs, the total impedance as seen by the voltage source

3. Use Phasors analysis to calculate the following for this single phase, AC steady-state circuit: • a. Z1, Z2, and Z3 as complex impedances in Ohms b. The parallel combination Z2//Z3 c. Zs, the total impedance as seen by the voltage source

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 Statement: Use phasor analysis to calculate the following for this single-phase AC steady-state circuit: a. \( Z_1, Z_2, \) and \( Z_3 \) as complex impedances in Ohms b. The parallel combination \( Z2 // Z3 \) c. \( Z_s, \) the total impedance as seen by the voltage source d. \( V_a, \) the node voltage at \( a, \) by any method e. \( P_4, \) the average power dissipated in the 4 Ohm resistor ### Circuit Description: The circuit consists of the following components: - **Voltage source:** \( 100 \cos(10t) \) volts - **Impedance \( Z_1 \):** A series combination of a resistor (1 Ohm) and an inductor (0.9 H) - **Impedance \( Z_2 \):** A capacitor (1/40 F) - **Impedance \( Z_3 \):** A series combination of a resistor (4 Ohm) and an inductor (0.4 H) The circuit is powered by an AC voltage source with a cosine waveform. The source current is \( I_s \), which enters the circuit through \( Z_1 \) and proceeds to the node labeled \( a \). The node voltage \( V_a \) is measured across the impedance \( Z_2 \) and \( Z_3 \), which are connected in parallel. ### Analysis Requirements: 1. **Complex Impedances Calculation:** - Determine the complex impedance for each component using phasor analysis. 2. **Parallel Combination:** - Calculate the equivalent impedance for \( Z_2 \) and \( Z_3 \). 3. **Total Impedance:** - Find the total impedance \( Z_s \) as experienced by the voltage source. 4. **Node Voltage Calculation:** - Calculate the node voltage \( V_a \) using any suitable analysis method. 5. **Average Power:** - Determine the average power (\( P_4 \)) dissipated by the 4 Ohm resistor in \( Z_3 \).
Transcribed Image Text:### Problem Statement: Use phasor analysis to calculate the following for this single-phase AC steady-state circuit: a. \( Z_1, Z_2, \) and \( Z_3 \) as complex impedances in Ohms b. The parallel combination \( Z2 // Z3 \) c. \( Z_s, \) the total impedance as seen by the voltage source d. \( V_a, \) the node voltage at \( a, \) by any method e. \( P_4, \) the average power dissipated in the 4 Ohm resistor ### Circuit Description: The circuit consists of the following components: - **Voltage source:** \( 100 \cos(10t) \) volts - **Impedance \( Z_1 \):** A series combination of a resistor (1 Ohm) and an inductor (0.9 H) - **Impedance \( Z_2 \):** A capacitor (1/40 F) - **Impedance \( Z_3 \):** A series combination of a resistor (4 Ohm) and an inductor (0.4 H) The circuit is powered by an AC voltage source with a cosine waveform. The source current is \( I_s \), which enters the circuit through \( Z_1 \) and proceeds to the node labeled \( a \). The node voltage \( V_a \) is measured across the impedance \( Z_2 \) and \( Z_3 \), which are connected in parallel. ### Analysis Requirements: 1. **Complex Impedances Calculation:** - Determine the complex impedance for each component using phasor analysis. 2. **Parallel Combination:** - Calculate the equivalent impedance for \( Z_2 \) and \( Z_3 \). 3. **Total Impedance:** - Find the total impedance \( Z_s \) as experienced by the voltage source. 4. **Node Voltage Calculation:** - Calculate the node voltage \( V_a \) using any suitable analysis method. 5. **Average Power:** - Determine the average power (\( P_4 \)) dissipated by the 4 Ohm resistor in \( Z_3 \).
Expert Solution
Step 1

given that a circuit with resistances, capacitances and inductances with an AC source.

 

NOTE : 

   As per our company guidelines we are supposed to answer first 3 sub-parts only. kindly re-post other parts in the next question.

 

here we have to find the impedances in complex form.

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