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?

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?

• A. 200 + j188
• B. 200 + j100
• C. 100 + j200
• D. 188 + j200

Answer: (A)

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 \,

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 ,