What is the impedance of a capacitive circuit to 20kHz frequency if it's reactance is 400Ohms and it's capacitance is 0.032microF?

The impedance of a capacitive circuit can be calculated using the formula:

Z = 1 / (2πfC)

Where:
Z = Impedance (in ohms)
π = Pi (approximately 3.14159)
f = Frequency (in hertz)
C = Capacitance (in farads)

Given:
Reactance (Xc) = 400 ohms
Capacitance (C) = 0.032 microfarads = 0.032 × 10^(-6) farads
Frequency (f) = 20 kHz = 20 × 10^3 hertz

First, convert the capacitance from microfarads to farads:
C = 0.032 × 10^(-6) = 3.2 × 10^(-8) farads

Now, substitute the values into the formula:
Z = 1 / (2πfC)
Z = 1 / (2 × 3.14159 × 20 × 10^3 × 3.2 × 10^(-8))
Z ≈ 1 / (6.28318 × 6.4 × 10^(-4))
Z ≈ 1 / 0.004023
Z ≈ 248.3 ohms

Therefore, the impedance of the capacitive circuit at a frequency of 20 kHz is approximately 248.3 ohms.