A capacitor has a capacitive reactance of 22 Ω when connected across a 120 V, 60 Hz supply. Calculate the capacitance in microfarads.
Question
A capacitor has a capacitive reactance of 22 Ω when connected across a 120 V, 60 Hz supply. Calculate the capacitance in microfarads.
Solution
Sure, to calculate the capacitance, we can use the formula for capacitive reactance which is:
Xc = 1 / (2πfC)
Where: Xc is the capacitive reactance (22 Ω in this case), f is the frequency (60 Hz in this case), and C is the capacitance, which we are trying to find.
Rearranging the formula to solve for C gives us:
C = 1 / (2πfXc)
Substituting the given values into the formula gives us:
C = 1 / (2 * π * 60 Hz * 22 Ω)
Solving this gives us a capacitance of approximately 0.0000012 Farads, or 1.2 microfarads.
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