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Calculate rms current amplitudes for the complex circuit

Calculate rms current amplitudes for the complex circuit

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 rms current amplitudes for the complex circuit

The image displays an electrical circuit diagram featuring the following components: 1. **VS (Voltage Source):** - Specification: 1.414 Vpk (Volts peak) - Frequency: 1 kHz - Phase: 0 degrees 2. **R1 (Resistor):** - Resistance: 400 ohms (Ω) 3. **C1 (Capacitor):** - Capacitance: 53.05 nF (nanofarads) - Initial Condition: Initial charge (IC) is 0V 4. **XMM1 (Voltmeter):** - Connected in parallel across the resistor R1 to measure the voltage. **Circuit Description:** - The circuit consists of a sine wave voltage source (VS) with a peak voltage of 1.414 V, a frequency of 1 kHz, and no phase shift. - The source is connected to a series resistor (R1) followed by a capacitor (C1). - The voltmeter (XMM1) is used to measure the voltage across the resistor R1. - The ground symbol indicates a common reference point for the circuit, ensuring that all components are electrically connected to the same voltage level. This setup is commonly used in RC (Resistor-Capacitor) circuits to study the behavior of capacitors in AC circuits, analyzing voltage, current, and phase relationships.
Transcribed Image Text:The image displays an electrical circuit diagram featuring the following components: 1. **VS (Voltage Source):** - Specification: 1.414 Vpk (Volts peak) - Frequency: 1 kHz - Phase: 0 degrees 2. **R1 (Resistor):** - Resistance: 400 ohms (Ω) 3. **C1 (Capacitor):** - Capacitance: 53.05 nF (nanofarads) - Initial Condition: Initial charge (IC) is 0V 4. **XMM1 (Voltmeter):** - Connected in parallel across the resistor R1 to measure the voltage. **Circuit Description:** - The circuit consists of a sine wave voltage source (VS) with a peak voltage of 1.414 V, a frequency of 1 kHz, and no phase shift. - The source is connected to a series resistor (R1) followed by a capacitor (C1). - The voltmeter (XMM1) is used to measure the voltage across the resistor R1. - The ground symbol indicates a common reference point for the circuit, ensuring that all components are electrically connected to the same voltage level. This setup is commonly used in RC (Resistor-Capacitor) circuits to study the behavior of capacitors in AC circuits, analyzing voltage, current, and phase relationships.
**Table: AC Circuit Analysis for Example Circuit** This table displays values related to the analysis of an AC circuit at different frequencies. It includes calculations for capacitive reactance, total impedance, peak current, and root mean square (RMS) current. | Frequency (f) | \( X_{C1} = 1/(2\pi fC_1) \) | \( Z_T = R_1 - jX_{C1} \) | \( Z = \sqrt{R_1^2 + X_{C1}^2} \) | \( I_T(\text{pk}) = V_S / Z \) | \( I_T(\text{rms}) = 0.707 \times I_T(\text{pk}) \) | |---------------|-------------------------------|----------------------------|--------------------------------|-------------------------------|-----------------------------------| | 1 kHz | | | | | | | 2 kHz | | | | | | | 3 kHz | | | | | | | 4 kHz | | | | | | | 5 kHz | | | | | | | 6 kHz | | | | | | | 7 kHz | | | | | | | 8 kHz | | | | | | | 9 kHz | | | | | | | 10 kHz | | | | | | **Explanation:** - **\( X_{C1} \)**: Capacitive reactance is a measure of a capacitor's opposition to changes in voltage and is dependent on frequency \( f \) and capacitance \( C_1 \). - **\( Z_T \) (Total Impedance)**: Represents the complex total impedance of the circuit, accounting for resistance \( R_1 \) and the imaginary part \( jX_{C1} \). - **\( Z \)**: The magnitude of the total impedance, calculated using the Pythagorean theorem, to determine the overall opposition in the circuit. - **\( I_T(\text{pk}) \) (Peak Current)**: Obtained by dividing the source voltage \( V_S
Transcribed Image Text:**Table: AC Circuit Analysis for Example Circuit** This table displays values related to the analysis of an AC circuit at different frequencies. It includes calculations for capacitive reactance, total impedance, peak current, and root mean square (RMS) current. | Frequency (f) | \( X_{C1} = 1/(2\pi fC_1) \) | \( Z_T = R_1 - jX_{C1} \) | \( Z = \sqrt{R_1^2 + X_{C1}^2} \) | \( I_T(\text{pk}) = V_S / Z \) | \( I_T(\text{rms}) = 0.707 \times I_T(\text{pk}) \) | |---------------|-------------------------------|----------------------------|--------------------------------|-------------------------------|-----------------------------------| | 1 kHz | | | | | | | 2 kHz | | | | | | | 3 kHz | | | | | | | 4 kHz | | | | | | | 5 kHz | | | | | | | 6 kHz | | | | | | | 7 kHz | | | | | | | 8 kHz | | | | | | | 9 kHz | | | | | | | 10 kHz | | | | | | **Explanation:** - **\( X_{C1} \)**: Capacitive reactance is a measure of a capacitor's opposition to changes in voltage and is dependent on frequency \( f \) and capacitance \( C_1 \). - **\( Z_T \) (Total Impedance)**: Represents the complex total impedance of the circuit, accounting for resistance \( R_1 \) and the imaginary part \( jX_{C1} \). - **\( Z \)**: The magnitude of the total impedance, calculated using the Pythagorean theorem, to determine the overall opposition in the circuit. - **\( I_T(\text{pk}) \) (Peak Current)**: Obtained by dividing the source voltage \( V_S
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