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Circuit Value XLI XCI ZEQ=XL | XCI ZT=R₁+ZEQ IT=Vs/ZT VOUTVRI IT R₁ f=500 Hz f=5 kHz f=50 kHz

Circuit Value XLI XCI ZEQ=XL | XCI ZT=R₁+ZEQ IT=Vs/ZT VOUTVRI IT R₁ 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 output voltage change as the frequency increases from 500Hz to 50 KHz

This schematic diagram represents an LC filter circuit. **Components:** 1. **Source Voltage (VS):** - 10 V peak - Frequency: 1 kHz - Phase: 0 degrees 2. **Capacitor (C1):** - Capacitance: 30 nF - Initial Condition (IC) = 0V 3. **Inductor (L1):** - Inductance: 30 mH - Initial Condition (IC) = 0A 4. **Resistor (R1):** - Resistance: 1 kΩ **Functionality:** - **Input Source:** The AC source generates a sinusoidal input with a peak voltage of 10 V at a frequency of 1 kHz and an initial phase angle of 0 degrees. - **LC Circuit:** The LC filter is formed by the capacitor (C1) and inductor (L1) connected in parallel. This configuration is typically used to filter or smooth specific frequency components from the input signal. - **Output (VOUT):** The output voltage is taken across the LC filter and resistor (R1), grounded on one side. The circuit's response to the 1 kHz signal will depend on the resonant frequency of the LC components. This LC circuit can be analyzed to understand its filtering properties, impedance characteristics, and how it affects the signal passing through it based on the given frequency and component values.
Transcribed Image Text:This schematic diagram represents an LC filter circuit. **Components:** 1. **Source Voltage (VS):** - 10 V peak - Frequency: 1 kHz - Phase: 0 degrees 2. **Capacitor (C1):** - Capacitance: 30 nF - Initial Condition (IC) = 0V 3. **Inductor (L1):** - Inductance: 30 mH - Initial Condition (IC) = 0A 4. **Resistor (R1):** - Resistance: 1 kΩ **Functionality:** - **Input Source:** The AC source generates a sinusoidal input with a peak voltage of 10 V at a frequency of 1 kHz and an initial phase angle of 0 degrees. - **LC Circuit:** The LC filter is formed by the capacitor (C1) and inductor (L1) connected in parallel. This configuration is typically used to filter or smooth specific frequency components from the input signal. - **Output (VOUT):** The output voltage is taken across the LC filter and resistor (R1), grounded on one side. The circuit's response to the 1 kHz signal will depend on the resonant frequency of the LC components. This LC circuit can be analyzed to understand its filtering properties, impedance characteristics, and how it affects the signal passing through it based on the given frequency and component values.
The table provided is for an electrical circuit analysis, displaying calculations at different frequencies (500 Hz, 5 kHz, and 50 kHz). The table is structured with the following rows and columns: ### Columns: 1. **Circuit Value**: Description of the parameter. 2. **f = 500 Hz**: Results for a frequency of 500 Hz. 3. **f = 5 kHz**: Results for a frequency of 5 kHz. 4. **f = 50 kHz**: Results for a frequency of 50 kHz. ### Rows: 1. **\( X_{L1} \)**: Inductive reactance. 2. **\( X_{C1} \)**: Capacitive reactance. 3. **\( Z_{EQ} = X_{L1} \| X_{C1} \)**: Equivalent impedance for the inductive and capacitive reactance in parallel. 4. **\( Z_{T} = R_1 + Z_{EQ} \)**: Total impedance, combining resistor \( R_1 \) and equivalent impedance \( Z_{EQ} \). 5. **\( I_{T} = V_{S} / Z_{T} \)**: Total current, calculated using source voltage \( V_S \) and total impedance \( Z_T \). 6. **\( V_{OUT} = V_{R1} = I_{T} \times R_1 \)**: Output voltage across resistor \( R_1 \), calculated using total current \( I_T \) and resistor \( R_1 \). ### Explanation: - The table is empty, indicating that the calculations have not yet been filled in for each frequency. - **Inductive Reactance \( X_{L1} \)** and **Capacitive Reactance \( X_{C1} \)** calculations will vary based on the frequency. - **Equivalent Impedance \( Z_{EQ} \)** combines the effects of both reactances in parallel. - **Total Impedance \( Z_T \)** adds the effect of the resistor to the equivalent impedance. - **Total Current \( I_T \)** is the result of applying Ohm's Law using total impedance. - **Output Voltage \( V_{OUT} \)** represents the voltage drop across the resistor. This table is useful for electrical engineering students learning circuit analysis techniques, particularly those involving reactance and impedance at different frequencies.
Transcribed Image Text:The table provided is for an electrical circuit analysis, displaying calculations at different frequencies (500 Hz, 5 kHz, and 50 kHz). The table is structured with the following rows and columns: ### Columns: 1. **Circuit Value**: Description of the parameter. 2. **f = 500 Hz**: Results for a frequency of 500 Hz. 3. **f = 5 kHz**: Results for a frequency of 5 kHz. 4. **f = 50 kHz**: Results for a frequency of 50 kHz. ### Rows: 1. **\( X_{L1} \)**: Inductive reactance. 2. **\( X_{C1} \)**: Capacitive reactance. 3. **\( Z_{EQ} = X_{L1} \| X_{C1} \)**: Equivalent impedance for the inductive and capacitive reactance in parallel. 4. **\( Z_{T} = R_1 + Z_{EQ} \)**: Total impedance, combining resistor \( R_1 \) and equivalent impedance \( Z_{EQ} \). 5. **\( I_{T} = V_{S} / Z_{T} \)**: Total current, calculated using source voltage \( V_S \) and total impedance \( Z_T \). 6. **\( V_{OUT} = V_{R1} = I_{T} \times R_1 \)**: Output voltage across resistor \( R_1 \), calculated using total current \( I_T \) and resistor \( R_1 \). ### Explanation: - The table is empty, indicating that the calculations have not yet been filled in for each frequency. - **Inductive Reactance \( X_{L1} \)** and **Capacitive Reactance \( X_{C1} \)** calculations will vary based on the frequency. - **Equivalent Impedance \( Z_{EQ} \)** combines the effects of both reactances in parallel. - **Total Impedance \( Z_T \)** adds the effect of the resistor to the equivalent impedance. - **Total Current \( I_T \)** is the result of applying Ohm's Law using total impedance. - **Output Voltage \( V_{OUT} \)** represents the voltage drop across the resistor. This table is useful for electrical engineering students learning circuit analysis techniques, particularly those involving reactance and impedance at different frequencies.
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