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

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

Options:

Correct Answer: 2652Ω

Solution:

The impedance of a capacitor is given by Z = 1 / (jωC). For 60Hz and 10μF, Z = 1 / (j * 2π * 60 * 10e-6) ≈ 2652Ω.

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

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

Step 1: Understand that impedance (Z) of a capacitor is calculated using the formula Z = 1 / (jωC).
Step 2: Identify the frequency (f) given in the question, which is 60Hz.
Step 3: Convert the frequency to angular frequency (ω) using the formula ω = 2πf. So, ω = 2π * 60.
Step 4: Calculate ω: ω = 2 * 3.14 * 60 ≈ 376.99 rad/s.
Step 5: Identify the capacitance (C) given in the question, which is 10μF (microfarads). Convert this to farads: C = 10 * 10^-6 F = 10e-6 F.
Step 6: Substitute ω and C into the impedance formula: Z = 1 / (j * 376.99 * 10e-6).
Step 7: Calculate the denominator: j * 376.99 * 10e-6 ≈ j * 0.00037699.
Step 8: Now calculate Z: Z = 1 / (j * 0.00037699).
Step 9: The magnitude of Z is approximately 2652Ω.

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