Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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**Educational Exercise: RC Low Pass Filter Analysis**

1. **Capacitance Calculation:**
   - A low pass RC filter using a 1k ohm resistor is operating at 20Hz and shows a 3dB drop in power from its max power at 0 Hz. Find its capacitance to the hundredths place. Write only the numerical part of your answer in µF: ________ µF.

2. **Cutoff Frequency and Reactance Relationship:**
   - This RC filter is powered by a 100V AC source. At cutoff frequency, what is the relationship to the resistance?
     - a) Xc = 0
     - b) Xc = R
     - c) Xc = infinite 
   - Enter the letter of the correct answer: ________

3. **Peak Voltage Calculation:**
   - At the operating point where Xc = R, calculate the peak voltage to the tenths place across the capacitor using voltage division and assuming an AC source of 100 V.
   - ________ Volts

4. **Peak Current Calculation:**
   - Given a peak voltage of 70.7V across a 22 µF capacitor in an RC low pass filter, what is the peak current in the circuit at 20Hz operating frequency? Enter the numerical part of your answer rounded to the ones place in mA: ________ mA

5. **Phase Shift at Cutoff Frequency:**
   - At the RC low pass filter cutoff frequency, the phase shift between current and voltage is always ________ deg. (*Be careful to include the appropriate sign.*) 

**Note:** Ensure each calculation is based on the understanding of RC filter fundamentals including reactance, impedance, and phase relationships.
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Transcribed Image Text:**Educational Exercise: RC Low Pass Filter Analysis** 1. **Capacitance Calculation:** - A low pass RC filter using a 1k ohm resistor is operating at 20Hz and shows a 3dB drop in power from its max power at 0 Hz. Find its capacitance to the hundredths place. Write only the numerical part of your answer in µF: ________ µF. 2. **Cutoff Frequency and Reactance Relationship:** - This RC filter is powered by a 100V AC source. At cutoff frequency, what is the relationship to the resistance? - a) Xc = 0 - b) Xc = R - c) Xc = infinite - Enter the letter of the correct answer: ________ 3. **Peak Voltage Calculation:** - At the operating point where Xc = R, calculate the peak voltage to the tenths place across the capacitor using voltage division and assuming an AC source of 100 V. - ________ Volts 4. **Peak Current Calculation:** - Given a peak voltage of 70.7V across a 22 µF capacitor in an RC low pass filter, what is the peak current in the circuit at 20Hz operating frequency? Enter the numerical part of your answer rounded to the ones place in mA: ________ mA 5. **Phase Shift at Cutoff Frequency:** - At the RC low pass filter cutoff frequency, the phase shift between current and voltage is always ________ deg. (*Be careful to include the appropriate sign.*) **Note:** Ensure each calculation is based on the understanding of RC filter fundamentals including reactance, impedance, and phase relationships.
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