6) Consider a low-pass filter made of a 1400 resistor and a C = 9μF capacitor. If the input rms current is 1A at a frequency of 55Hz what is the output voltage?
6) Consider a low-pass filter made of a 1400 resistor and a C = 9μF capacitor. If the input rms current is 1A at a frequency of 55Hz what is the output voltage?
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![**Problem 6: Low-Pass Filter Voltage Calculation**
Consider a low-pass filter composed of a 140Ω resistor and a capacitor with capacitance \( C = 9\mu F \). If the input rms (root mean square) current is 1A at a frequency of 55Hz, what is the output voltage?
This problem requires knowledge of electrical circuits, specifically the behavior of low-pass filters, to calculate the output voltage based on the given parameters.
To solve this, you would need to:
1. Calculate the capacitive reactance (\( X_C \)) using the formula:
\[
X_C = \frac{1}{2\pi fC}
\]
2. Calculate the total impedance (\( Z \)) of the filter:
\[
Z = \sqrt{R^2 + X_C^2}
\]
3. Use Ohm’s Law to find the output voltage (\( V_{\text{out}} \)):
\[
V_{\text{out}} = I \times Z
\]
Where:
- \( f \) is the frequency (55Hz),
- \( R \) is the resistance (140Ω),
- \( I \) is the rms current (1A),
- \( C \) is the capacitance (9μF).
This calculation involves circuit analysis skills and understanding reactance in AC circuits.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf5ca60f-6906-44bf-a492-477ae53fc791%2F2a60fc47-539c-4176-b4a3-19141a7d9e26%2F3m91is9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 6: Low-Pass Filter Voltage Calculation**
Consider a low-pass filter composed of a 140Ω resistor and a capacitor with capacitance \( C = 9\mu F \). If the input rms (root mean square) current is 1A at a frequency of 55Hz, what is the output voltage?
This problem requires knowledge of electrical circuits, specifically the behavior of low-pass filters, to calculate the output voltage based on the given parameters.
To solve this, you would need to:
1. Calculate the capacitive reactance (\( X_C \)) using the formula:
\[
X_C = \frac{1}{2\pi fC}
\]
2. Calculate the total impedance (\( Z \)) of the filter:
\[
Z = \sqrt{R^2 + X_C^2}
\]
3. Use Ohm’s Law to find the output voltage (\( V_{\text{out}} \)):
\[
V_{\text{out}} = I \times Z
\]
Where:
- \( f \) is the frequency (55Hz),
- \( R \) is the resistance (140Ω),
- \( I \) is the rms current (1A),
- \( C \) is the capacitance (9μF).
This calculation involves circuit analysis skills and understanding reactance in AC circuits.
Expert Solution
Step 1
Given Data:
Resistance of resistor
Capacitance of capicitor
RMS current
Frequency
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