What is the impedance of a network composed of a 0.1-microhenry inductor in series with a 20-ohm resistor, at 30 MHz?

To determine the impedance of a network composed of a inductor and a resistor, you need to compute both the resistive and the reactive components of the impedance.

Firstly, calculate the inductive reactance (X_L) of the inductor using the formula:

[ X_L = 2 \pi f L ]

Where:

• (f) is the frequency in hertz,

• (L) is the inductance in henries.

In this case:

• (f = 30 \text{ MHz} = 30 \times 10^6 \text{ Hz})

• (L = 0.1 \text{ microhenries} = 0.1 \times 10^{-6} \text{ H})

Now, substituting these values into the formula:

[ X_L = 2 \pi (30 \times 10^6) (0.1 \times 10^{-6}) ]

Calculating this gives:

[ X_L = 2 \pi (30 \times 0.1) = 2 \pi (3) = 6 \pi \approx 18.85 \text{ ohms} ]

This value can be rounded to approximately