You are designing a low-pass RC filter with a cutoff frequency of 1 kHz. If you have a 10kΩ resistor, what capacitance value is required to achieve this cutoff frequency?
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To calculate the capacitance required for a low-pass RC filter with a cutoff frequency of 1 kHz, use the following formula:
C = 1 / (2π * f * R)
Where:
C = Capacitance value in Farads
π = Pi (approximately 3.14159)
f = Cutoff frequency in Hertz
R = Resistor value in Ohms
Given:
Cutoff frequency (f) = 1 kHz = 1000 Hz
Resistor (R) = 10 kΩ = 10000 Ω
Plug the values into the formula:
C = 1 / (2 * π * 1000 * 10000)
C ≈ 1 / (62831.85)
C ≈ 15.92 microfarads
Therefore, to achieve a cutoff frequency of 1 kHz with a 10 kΩ resistor, you would need a capacitor with a value of approximately 15.92 microfarads.
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