At what frequency is a 0.0001 uF capacitor operating if its reactance is 45 k ohm?
To determine the frequency at which a capacitor with a reactance of 45 kΩ is operating, we can use the formula for capacitive reactance:
Reactance (Xc) = 1 / (2 * π * f * C)
Where:
Xc = Capacitive reactance (in ohms)
f = Frequency (in hertz)
C = Capacitance (in farads)
In this case, we are given the capacitance (C) as 0.0001 µF (microfarads or 10^(-7) farads) and the reactance (Xc) as 45 kΩ (kiloohms or 10^3 ohms).
Plugging in the values into the formula, we have:
45 kΩ = 1 / (2 * π * f * 0.0001 µF)
To solve for frequency (f), we can rearrange the equation:
f = 1 / (2 * π * 45 kΩ * 0.0001 µF)
Let's now calculate the frequency:
f = 1 / (2 * π * 45,000 Ω * 0.0000001 F)
Simplifying further:
f = 1 / (2 * π * 0.0045)
f ≈ 35.28 Hz
Therefore, the 0.0001 µF capacitor is operating at approximately 35.28 Hz.