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Determine Impedance magnitude and phase angle.

Determine Impedance magnitude and phase angle.

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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**Circuit Analysis: Impedance and Phase Angle Determination** **Objective**: Determine the impedance magnitude and phase angle. **Given**: - Voltage source (\(V_s\)): 18V RMS - Frequency (\(f\)): 2 kHz **Circuit Components**: - Two capacitors: - Capacitor 1: 0.1 µF - Capacitor 2: 0.22 µF - Three resistors: - Resistor 1: 370 Ω - Resistor 2: 320 Ω - Resistor 3: 650 Ω **Configuration**: - The circuit includes a parallel configuration of capacitors and resistors. - The capacitors are placed in parallel with each other. - Resistor 1 (370 Ω) is connected in series with the parallel capacitors, followed by resistor 2 (320 Ω) in series, and finally resistor 3 (650 Ω) in parallel with resistor 2 and the capacitors. **Analysis**: To determine the overall impedance and phase angle of this circuit, perform the following steps: 1. **Calculate Capacitive Reactance** (\(X_C\)): - For Capacitor 1: \(X_{C1} = \frac{1}{2\pi f C_1}\) - For Capacitor 2: \(X_{C2} = \frac{1}{2\pi f C_2}\) 2. **Combine Impedances**: - Calculate the total impedance \(Z\) by combining the resistive and capacitive components. - Take into account the series and parallel configurations of the circuit elements. 3. **Determine Impedance Magnitude** (\(|Z|\)): - Use \( |Z| = \sqrt{R^2 + (X_L - X_C)^2} \) for the equivalent resistive and reactive parts. 4. **Determine Phase Angle** (\(\theta\)): - Use the formula \(\theta = \tan^{-1} \left(\frac{X}{R}\right)\) to find the phase shift caused by the reactive components. This analysis helps in understanding how the circuit will behave at a frequency of 2 kHz, including how much the current will lag or lead concerning the applied voltage due to the reactive components.
Transcribed Image Text:**Circuit Analysis: Impedance and Phase Angle Determination** **Objective**: Determine the impedance magnitude and phase angle. **Given**: - Voltage source (\(V_s\)): 18V RMS - Frequency (\(f\)): 2 kHz **Circuit Components**: - Two capacitors: - Capacitor 1: 0.1 µF - Capacitor 2: 0.22 µF - Three resistors: - Resistor 1: 370 Ω - Resistor 2: 320 Ω - Resistor 3: 650 Ω **Configuration**: - The circuit includes a parallel configuration of capacitors and resistors. - The capacitors are placed in parallel with each other. - Resistor 1 (370 Ω) is connected in series with the parallel capacitors, followed by resistor 2 (320 Ω) in series, and finally resistor 3 (650 Ω) in parallel with resistor 2 and the capacitors. **Analysis**: To determine the overall impedance and phase angle of this circuit, perform the following steps: 1. **Calculate Capacitive Reactance** (\(X_C\)): - For Capacitor 1: \(X_{C1} = \frac{1}{2\pi f C_1}\) - For Capacitor 2: \(X_{C2} = \frac{1}{2\pi f C_2}\) 2. **Combine Impedances**: - Calculate the total impedance \(Z\) by combining the resistive and capacitive components. - Take into account the series and parallel configurations of the circuit elements. 3. **Determine Impedance Magnitude** (\(|Z|\)): - Use \( |Z| = \sqrt{R^2 + (X_L - X_C)^2} \) for the equivalent resistive and reactive parts. 4. **Determine Phase Angle** (\(\theta\)): - Use the formula \(\theta = \tan^{-1} \left(\frac{X}{R}\right)\) to find the phase shift caused by the reactive components. This analysis helps in understanding how the circuit will behave at a frequency of 2 kHz, including how much the current will lag or lead concerning the applied voltage due to the reactive components.
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