In rectangular coordinates, what is the impedance of a network composed of a 1.0-millihenry inductor in series with a 200-ohm resistor, at 30 kHz?

To determine the impedance of a network that includes a 1.0-millihenry inductor in series with a 200-ohm resistor at a frequency of 30 kHz, it’s important to calculate the inductive reactance of the inductor.

The reactance of an inductor in a circuit is given by the formula:

[ X_L = 2\pi f L ]

where:

• ( X_L ) = inductive reactance in ohms,

• ( f ) = frequency in hertz (Hz),

• ( L ) = inductance in henries (H).

Given:

• ( L = 1.0 , \text{mH} = 1.0 \times 10^{-3} , \text{H} ),

• ( f = 30 , \text{kHz} = 30,000 , \text{Hz} ).

Now, substituting the values into the equation:

[ X_L = 2\pi(30,000)(1.0 \times 10^{-3}) ]

Calculating this gives:

[ X_L = 2\pi(30) \approx 188.5 ,