The impedance of a capacitor in the frequency domain is given by the formula:

Z = -j/(ωC)

where:
- j is the imaginary unit,
- ω is the angular frequency, and
- C is the capacitance.

First, we need to convert the frequency to angular frequency. The angular frequency ω is related to the frequency f by the formula:

ω = 2πf

So, for a frequency of 5 kHz, we have:

ω = 2π * 5000 = 31,400 rad/s

Next, we substitute ω and the capacitance C = 10 μF = 10^-5 F into the formula for Z:

Z = -j/(31,400 * 10^-5) = -j/0.314 = -j * 3.18 kΩ

The negative sign indicates that the phase angle is -90°. Therefore, the impedance of the capacitor is 3.18 kΩ

Question

The impedance of a capacitor in the frequency domain is given by the formula:

Z = -j/(ωC)

where:
- j is the imaginary unit,
- ω is the angular frequency, and
- C is the capacitance.

First, we need to convert the frequency to angular frequency. The angular frequency ω is related to the frequency f by the formula:

ω = 2πf

So, for a frequency of 5 kHz, we have:

ω = 2π * 5000 = 31,400 rad/s

Next, we substitute ω and the capacitance C = 10 μF = 10^-5 F into the formula for Z:

Z = -j/(31,400 * 10^-5) = -j/0.314 = -j * 3.18 kΩ

The negative sign indicates that the phase angle is -90°. Therefore, the impedance of the capacitor is 3.18 kΩ < -90°.

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