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a) Draw the Phasor diagram and approximate wave form. b) At what frequency the inductor and capacitor impedance have equal magnitude. c) What is the voltage across each element (R, L and C) at this frequency.

a) Draw the Phasor diagram and approximate wave form. b) At what frequency the inductor and capacitor impedance have equal magnitude. c) What is the voltage across each element (R, L and C) at this frequency.

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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## Circuit Analysis and Calculations ### Description The image depicts an electrical circuit consisting of a function generator which outputs a voltage given by \(5\sqrt{2} \cos(\omega t) V\). The circuit is connected in series with a capacitor of \(0.1 \, \mu F\), an inductor of \(0.4 \, H\), and a resistor of \(1k\, \Omega\). The voltage across the resistor is labeled as \( V_r \). ### Tasks 1. **Draw the Phasor Diagram and Approximate Waveform:** - The task involves creating a phasor diagram that graphically represents the phase relationship between the circuit elements. Additionally, one should sketch the approximate waveform for the circuit's response. 2. **Identify the Frequency at Which Inductor and Capacitor Impedance Are Equal:** - The task is to calculate the frequency at which the magnitudes of the reactances of the inductor and capacitor are equal. This condition marks the resonant frequency. 3. **Determine the Voltage Across Each Element (R, L, and C) at Resonance:** - Calculate the individual voltages across the resistor, inductor, and capacitor when the circuit operates at the resonant frequency. ### Explanation of Circuit Components - **Function Generator:** Provides an AC voltage source with an amplitude of \(5\sqrt{2} \, V\). - **Capacitor (0.1 \, \mu F):** Offers capacitive reactance which decreases with increasing frequency. - **Inductor (0.4 \, H):** Provides inductive reactance which increases with increasing frequency. - **Resistor (1k \, \Omega):** Dissipates energy in the form of heat and provides resistance to the flow of current. This setup is commonly used in studies of AC circuits, particularly in learning about resonance and frequency response.
Transcribed Image Text:## Circuit Analysis and Calculations ### Description The image depicts an electrical circuit consisting of a function generator which outputs a voltage given by \(5\sqrt{2} \cos(\omega t) V\). The circuit is connected in series with a capacitor of \(0.1 \, \mu F\), an inductor of \(0.4 \, H\), and a resistor of \(1k\, \Omega\). The voltage across the resistor is labeled as \( V_r \). ### Tasks 1. **Draw the Phasor Diagram and Approximate Waveform:** - The task involves creating a phasor diagram that graphically represents the phase relationship between the circuit elements. Additionally, one should sketch the approximate waveform for the circuit's response. 2. **Identify the Frequency at Which Inductor and Capacitor Impedance Are Equal:** - The task is to calculate the frequency at which the magnitudes of the reactances of the inductor and capacitor are equal. This condition marks the resonant frequency. 3. **Determine the Voltage Across Each Element (R, L, and C) at Resonance:** - Calculate the individual voltages across the resistor, inductor, and capacitor when the circuit operates at the resonant frequency. ### Explanation of Circuit Components - **Function Generator:** Provides an AC voltage source with an amplitude of \(5\sqrt{2} \, V\). - **Capacitor (0.1 \, \mu F):** Offers capacitive reactance which decreases with increasing frequency. - **Inductor (0.4 \, H):** Provides inductive reactance which increases with increasing frequency. - **Resistor (1k \, \Omega):** Dissipates energy in the form of heat and provides resistance to the flow of current. This setup is commonly used in studies of AC circuits, particularly in learning about resonance and frequency response.
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