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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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**Title: Analyzing an R-C Circuit** **Introduction:** Explore a fundamental problem in electrical engineering by analyzing an R-C (resistor-capacitor) circuit. We examine the given circuit with specified parameters and equations to determine various phasors and impedance. **Problem Statement:** Given the circuit in Figure 7.3a, we have: - Input Voltage: \( v_i(t) = 1.5 \sin(1000\pi t) \) [V] - Resistance: \( R = 6.8 \) [kΩ] - Capacitance: \( C = 0.01 \) [µF] **Tasks:** 1. **Find the Impedance Phasor \( Z_{RC} \):** 2. **Determine the Phasors \( V_i, V_R, \) and \( V_C \):** - \( V_i \): Phasor representing the input voltage. - \( V_R \): Phasor corresponding to the resistor voltage. - \( V_C \): Phasor corresponding to the capacitor voltage. 3. **Draw the Impedance and Voltage Phasor Diagrams:** - These diagrams visually represent the relationships between the various phasors and impedance in the circuit. **Detailed Explanation:** - **Impedance \( Z_{RC} \):** Impedance in an R-C circuit is a combination of resistive and capacitive effects, often represented in phasor form as \( Z = R + jX_C \), where \( X_C \) is the capacitive reactance. - **Phasors \( V_i, V_R, \) and \( V_C \):** Phasors are a representation of sinusoidal functions that consider both magnitude and phase angle. They simplify the analysis of AC circuits by converting differential equations into algebraic equations. - **Phasor Diagrams:** These diagrams illustrate the phase relationships between currents and voltages in AC circuits. Impedance and voltage phasors are drawn as vectors in a complex plane. **Conclusion:** This exercise demonstrates essential concepts in AC circuit analysis, including impedance calculation and the use of phasors to represent sinusoidal voltages and currents.
Transcribed Image Text:**Title: Analyzing an R-C Circuit** **Introduction:** Explore a fundamental problem in electrical engineering by analyzing an R-C (resistor-capacitor) circuit. We examine the given circuit with specified parameters and equations to determine various phasors and impedance. **Problem Statement:** Given the circuit in Figure 7.3a, we have: - Input Voltage: \( v_i(t) = 1.5 \sin(1000\pi t) \) [V] - Resistance: \( R = 6.8 \) [kΩ] - Capacitance: \( C = 0.01 \) [µF] **Tasks:** 1. **Find the Impedance Phasor \( Z_{RC} \):** 2. **Determine the Phasors \( V_i, V_R, \) and \( V_C \):** - \( V_i \): Phasor representing the input voltage. - \( V_R \): Phasor corresponding to the resistor voltage. - \( V_C \): Phasor corresponding to the capacitor voltage. 3. **Draw the Impedance and Voltage Phasor Diagrams:** - These diagrams visually represent the relationships between the various phasors and impedance in the circuit. **Detailed Explanation:** - **Impedance \( Z_{RC} \):** Impedance in an R-C circuit is a combination of resistive and capacitive effects, often represented in phasor form as \( Z = R + jX_C \), where \( X_C \) is the capacitive reactance. - **Phasors \( V_i, V_R, \) and \( V_C \):** Phasors are a representation of sinusoidal functions that consider both magnitude and phase angle. They simplify the analysis of AC circuits by converting differential equations into algebraic equations. - **Phasor Diagrams:** These diagrams illustrate the phase relationships between currents and voltages in AC circuits. Impedance and voltage phasors are drawn as vectors in a complex plane. **Conclusion:** This exercise demonstrates essential concepts in AC circuit analysis, including impedance calculation and the use of phasors to represent sinusoidal voltages and currents.
**Figure 7.3: Passive Low-pass Filters:** This image illustrates a simple passive low-pass filter circuit. The filter circuit comprises: - **Input Voltage Source \( v_i(t) \):** Represented by the sine wave symbol on the left, this is the input signal to the circuit. - **Resistor \( R \):** Connected in series with the input voltage source, it affects the impedance and frequency response of the circuit. The voltage across the resistor is labeled \( v_R(t) \) and the current passing through it is \( i(t) \). - **Capacitor \( C \):** Connected parallel to the output, it stores energy and allows the circuit to pass low-frequency signals while attenuating higher-frequency signals. - **Output Voltage \( v_C(t) = v_o(t) \):** Measured across the capacitor, this is the filtered signal. The circuit is grounded at point (a), establishing a reference point for the voltage levels in the circuit. This configuration is used to filter out high-frequency noise from signals, allowing only frequencies below a certain cutoff frequency to pass through, hence the term "low-pass filter."
Transcribed Image Text:**Figure 7.3: Passive Low-pass Filters:** This image illustrates a simple passive low-pass filter circuit. The filter circuit comprises: - **Input Voltage Source \( v_i(t) \):** Represented by the sine wave symbol on the left, this is the input signal to the circuit. - **Resistor \( R \):** Connected in series with the input voltage source, it affects the impedance and frequency response of the circuit. The voltage across the resistor is labeled \( v_R(t) \) and the current passing through it is \( i(t) \). - **Capacitor \( C \):** Connected parallel to the output, it stores energy and allows the circuit to pass low-frequency signals while attenuating higher-frequency signals. - **Output Voltage \( v_C(t) = v_o(t) \):** Measured across the capacitor, this is the filtered signal. The circuit is grounded at point (a), establishing a reference point for the voltage levels in the circuit. This configuration is used to filter out high-frequency noise from signals, allowing only frequencies below a certain cutoff frequency to pass through, hence the term "low-pass filter."
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