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Problem 3 For the circuit shown below consider us(t) = 40 cos(1000t + 60°) V: a) Find the phasors Is, VR, VL, and Vc. b) Construct a phasor diagram showing Vs, VR, VL, and Vc, and Is. What is the phase relationship between Vs and Is? is (1) V<(1) + 20 92 www + UR- 25 mH oooo + V₁ - +2 1 100 uF

Problem 3 For the circuit shown below consider us(t) = 40 cos(1000t + 60°) V: a) Find the phasors Is, VR, VL, and Vc. b) Construct a phasor diagram showing Vs, VR, VL, and Vc, and Is. What is the phase relationship between Vs and Is? is (1) V<(1) + 20 92 www + UR- 25 mH oooo + V₁ - +2 1 100 uF

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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**Problem 3** For the circuit shown below, consider \( v_s(t) = 40 \cos(1000t + 60^\circ) \) V: a) Find the phasors \( I_S, V_R, V_L, \) and \( V_C \). b) Construct a phasor diagram showing \( V_S, V_R, V_L, V_C, \) and \( I_S \). What is the phase relationship between \( V_S \) and \( I_S \)? **Circuit Description:** - The circuit is powered by a voltage source \( v_s(t) \). - The current flowing through the circuit is \( i_S(t) \). - The circuit includes a resistor with a resistance of 20 Ω, an inductor with an inductance of 25 mH, and a capacitor with a capacitance of 100 μF. - The voltages across the resistor, inductor, and capacitor are labeled \( v_R \), \( v_L \), and \( v_C \), respectively. **Instructions for Analyzing the Circuit:** 1. **Finding Phasors:** - Calculate the phasors for the current \( I_S \) and the voltages \( V_R \), \( V_L \), \( V_C \) using known circuit analysis techniques such as Ohm's Law and the impedance formulas for inductors and capacitors. 2. **Phasor Diagram:** - Draw a phasor diagram with vectors representing \( V_S, V_R, V_L, V_C, \) and \( I_S \). - Indicate the phase angles between these vectors, showing how \( V_S \) and \( I_S \) relate in terms of phase. *Note: Ensure correct calculation methods based on AC circuit analysis and phasor relationships.*
Transcribed Image Text:**Problem 3** For the circuit shown below, consider \( v_s(t) = 40 \cos(1000t + 60^\circ) \) V: a) Find the phasors \( I_S, V_R, V_L, \) and \( V_C \). b) Construct a phasor diagram showing \( V_S, V_R, V_L, V_C, \) and \( I_S \). What is the phase relationship between \( V_S \) and \( I_S \)? **Circuit Description:** - The circuit is powered by a voltage source \( v_s(t) \). - The current flowing through the circuit is \( i_S(t) \). - The circuit includes a resistor with a resistance of 20 Ω, an inductor with an inductance of 25 mH, and a capacitor with a capacitance of 100 μF. - The voltages across the resistor, inductor, and capacitor are labeled \( v_R \), \( v_L \), and \( v_C \), respectively. **Instructions for Analyzing the Circuit:** 1. **Finding Phasors:** - Calculate the phasors for the current \( I_S \) and the voltages \( V_R \), \( V_L \), \( V_C \) using known circuit analysis techniques such as Ohm's Law and the impedance formulas for inductors and capacitors. 2. **Phasor Diagram:** - Draw a phasor diagram with vectors representing \( V_S, V_R, V_L, V_C, \) and \( I_S \). - Indicate the phase angles between these vectors, showing how \( V_S \) and \( I_S \) relate in terms of phase. *Note: Ensure correct calculation methods based on AC circuit analysis and phasor relationships.*
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