What is the impedance of a capacitor at a frequency of 60 Hz with a capacitance

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Question: What is the impedance of a capacitor at a frequency of 60 Hz with a capacitance of 10 µF?

Options:

Correct Answer: 26.52 ohms

Solution:

The impedance (Z) of a capacitor is given by Z = 1 / (2 * π * f * C). Thus, Z = 1 / (2 * π * 60 * 10e-6) ≈ 265.2 ohms.

What is the impedance of a capacitor at a frequency of 60 Hz with a capacitance of 10 µF?

What is the impedance of a capacitor at a frequency of 60 Hz with a capacitance of 10 µF?

Step 1: Identify the formula for the impedance (Z) of a capacitor, which is Z = 1 / (2 * π * f * C).
Step 2: Note the values given in the question: frequency (f) = 60 Hz and capacitance (C) = 10 µF (which is 10e-6 F).
Step 3: Substitute the values into the formula: Z = 1 / (2 * π * 60 * 10e-6).
Step 4: Calculate the denominator: 2 * π * 60 * 10e-6.
Step 5: Perform the multiplication: 2 * π ≈ 6.2832, then 6.2832 * 60 ≈ 376.99, and finally 376.99 * 10e-6 ≈ 0.00037699.
Step 6: Now, calculate Z: Z = 1 / 0.00037699.
Step 7: Perform the division: Z ≈ 265.2 ohms.

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