In rectangular coordinates, what is the impedance of a network composed of a 0.1-microhenry inductor in series with a 30-ohm resistor, at 5 MHz?

To find the impedance of a network that includes a resistor and an inductor in series, we first need to calculate the inductive reactance of the inductor and then combine it with the resistance.

The inductive reactance (X_L) can be calculated 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, the values are:

• Frequency ( f = 5 , \text{MHz} = 5 \times 10^6 , \text{Hz} ),

• Inductance ( L = 0.1 , \mu H = 0.1 \times 10^{-6} , H ).

Plugging the values into the formula:

[

X_L = 2 \pi (5 \times 10^6) (0.1 \times 10^{-6})

]

Calculating this gives:

[

X_L = 2 \pi (5) (0.1) = 0.1 \times 10^{6} \times 10^{6.283