What is the impedance of a network composed of a 0.001-microfarad capacitor in series with a 400-ohm resistor, at 500 kHz?

To determine the impedance of a network that consists of a 0.001-microfarad capacitor in series with a 400-ohm resistor at a frequency of 500 kHz, we start by calculating the capacitive reactance (Xc) of the capacitor. The formula for capacitive reactance is given by:

[ X_c = \frac{1}{2 \pi f C} ]

Where:

• ( f ) is the frequency (in hertz),

• ( C ) is the capacitance (in farads).

Converting 0.001 microfarads to farads gives us:

[ 0.001 , \text{microfarads} = 0.001 \times 10^{-6} , \text{farads} = 1 \times 10^{-9} , \text{farads} ]

Now substituting in the values:

[ f = 500 \times 10^3 , \text{Hz} ]

[ C = 1 \times 10^{-9} , \text{F} ]

Calculating ( X_c ):

[ X_c = \frac{1}{2 \pi (500