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Circuit Value XLI XCI IRI=VS/R₁ IL-VS/XLI Ici=Vs/XCI IT IRI+j(ICI-IL) ZT=VS/IT f=500 Hz f=5 kHz f=50 kHz

Circuit Value XLI XCI IRI=VS/R₁ IL-VS/XLI Ici=Vs/XCI IT IRI+j(ICI-IL) ZT=VS/IT f=500 Hz f=5 kHz f=50 kHz

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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Calculate circuit values below. How does the total circuit impedence change as the frequency increases from 500 HZ to 50 Khz? How does the total current change as those frequencies increase?

### Circuit Diagram Description The schematic diagram displayed is a simple RLC (Resistor-Inductor-Capacitor) series circuit. It contains the following components: 1. **Voltage Source (VS):** - **Value:** 10 Volts peak (Vpk) - **Frequency:** 1 kHz - **Phase:** 0 degrees - The source provides an AC signal at 1 kHz with a peak voltage of 10 volts, starting at 0 degrees phase angle. 2. **Capacitor (C1):** - **Capacitance:** 30 nanoFarads (nF) - **Initial Condition (IC):** 0 Volts (V) - The capacitor is initially uncharged. 3. **Inductor (L1):** - **Inductance:** 30 milliHenries (mH) - **Initial Condition (IC):** 0 Amperes (A) - The inductor has no initial current flowing through it. 4. **Resistor (R1):** - **Resistance:** 1 kiloOhm (kΩ) - The resistor provides a constant resistance to the AC circuit. ### Explanation This RLC circuit is commonly used to study the behavior of AC circuits with reactive components (inductors and capacitors). Key characteristics such as impedance, phase angle, and resonance can be analyzed using such a setup. Understanding these interactions is crucial in designing circuits for various applications in electronics and communication systems.
Transcribed Image Text:### Circuit Diagram Description The schematic diagram displayed is a simple RLC (Resistor-Inductor-Capacitor) series circuit. It contains the following components: 1. **Voltage Source (VS):** - **Value:** 10 Volts peak (Vpk) - **Frequency:** 1 kHz - **Phase:** 0 degrees - The source provides an AC signal at 1 kHz with a peak voltage of 10 volts, starting at 0 degrees phase angle. 2. **Capacitor (C1):** - **Capacitance:** 30 nanoFarads (nF) - **Initial Condition (IC):** 0 Volts (V) - The capacitor is initially uncharged. 3. **Inductor (L1):** - **Inductance:** 30 milliHenries (mH) - **Initial Condition (IC):** 0 Amperes (A) - The inductor has no initial current flowing through it. 4. **Resistor (R1):** - **Resistance:** 1 kiloOhm (kΩ) - The resistor provides a constant resistance to the AC circuit. ### Explanation This RLC circuit is commonly used to study the behavior of AC circuits with reactive components (inductors and capacitors). Key characteristics such as impedance, phase angle, and resonance can be analyzed using such a setup. Understanding these interactions is crucial in designing circuits for various applications in electronics and communication systems.
**Circuit Analysis Table** This table provides a structured approach to analyzing a circuit at different frequencies, specifically 500 Hz, 5 kHz, and 50 kHz. It lists the following parameters and equations: - **\( X_{L1} \)**: Inductive reactance - **\( X_{C1} \)**: Capacitive reactance - **\( I_{R1} = V_S / R_1 \)**: Current through the resistor - **\( I_{L1} = V_S / X_{L1} \)**: Current through the inductor - **\( I_{C1} = V_S / X_{C1} \)**: Current through the capacitor - **\( I_T = I_{R1} + j(I_{C1} - I_{L1}) \)**: Total current in the circuit, accounting for phase differences - **\( Z_T = V_S / I_T \)**: Total impedance of the circuit This table does not contain specific numerical values but leaves space to calculate and fill in these values at each specified frequency. This allows for analysis of how the circuit behavior changes as the frequency varies.
Transcribed Image Text:**Circuit Analysis Table** This table provides a structured approach to analyzing a circuit at different frequencies, specifically 500 Hz, 5 kHz, and 50 kHz. It lists the following parameters and equations: - **\( X_{L1} \)**: Inductive reactance - **\( X_{C1} \)**: Capacitive reactance - **\( I_{R1} = V_S / R_1 \)**: Current through the resistor - **\( I_{L1} = V_S / X_{L1} \)**: Current through the inductor - **\( I_{C1} = V_S / X_{C1} \)**: Current through the capacitor - **\( I_T = I_{R1} + j(I_{C1} - I_{L1}) \)**: Total current in the circuit, accounting for phase differences - **\( Z_T = V_S / I_T \)**: Total impedance of the circuit This table does not contain specific numerical values but leaves space to calculate and fill in these values at each specified frequency. This allows for analysis of how the circuit behavior changes as the frequency varies.
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