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

Specify your answer in rectangular coordinates.

20 +j19

From codygasser:

The impedance of an inductor, specified XL, is found using this equation:
    XL = 2 ∗ \(\pi\) ∗ frequency ∗ inductance
    XL = 2 ∗ \(\pi\) ∗ 30 MHz ∗ 0.1 uH
    XL = 18.85 Ω

Inductive Impedance is imaginary, specified "j" or "i", and it has a positive 90° degree angle, which means it gets added to the real resistance or 20 Ω:
20 + j19 Ω

For more information, please see Ham Radio School site article called Complex Impedance Part 3: Putting It All Together.

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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?

30 +j3

From codygasser:

The impedance of an inductor, specified XL, is found using this equation:
    XL = 2 ∗ \(\pi\) ∗ frequency ∗ inductance
    XL = 2 ∗ \(\pi\) ∗ 5 MHz ∗ 0.1uH
    XL = 3.14 Ω ohms

Inductive Impedance is imaginary, specified "j" or "i", and it has a positive 90° degree angle, which means it gets added to the real resistance or 30 Ω:
30 + j3 Ω Ohms

For more information, please see Ham Radio School site article called Complex Impedance Part 3: Putting It All Together.

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In rectangular coordinates, what is the impedance of a network composed of a
10-microhenry inductor in series with a
40-ohm resistor, at
500 MHz?

40 +j31400

From kd9fni:

Zr = 40 ohms

Zl = jwL
Zl = j (500 MHz) ∗ (2 x \(\pi\)) ∗ (10 uH)
Zl = j3140e6 ∗ 10e^-6
Zl = j31400 Ω ohms

Ztotal = Zr + Zl = 40 + j31400 Ω ohms

For more information, please see Ham Radio School site article called Complex Impedance Part 3: Putting It All Together.

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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?

200 + j188

From codygasser:

The impedance of an inductor, specified XL, is found using this equation:
    XL = 2 ∗ \(\pi\) ∗ frequency ∗ inductance
    XL = 2 ∗ \(\pi\) ∗ 30 MHz ∗ 1 mH
    XL = 188 Ω

Inductive Impedance is imaginary, specified "j" or "i", and it has a positive 90° degree angle, which means it gets added to the real resistance or 200 Ω:
200 + j188 Ω

For more information, please see Ham Radio School site article called Complex Impedance Part 3: Putting It All Together.

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In rectangular coordinates, what is the impedance of a network composed of a
0.01-microfarad capacitor in parallel with a
300-ohm resistor, at
50 kHz?***

159 - j150

From jrmills2468:

Formula for parallel RC circuit calculations can be found at the middle of the linked page

Please see Web Archive Org site for the article Parallel RC Circuits The Circuit

To save time you only need to remember the negative sign and then calculate either the real or imaginary part.

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

400 - j318

From kd7bbc:

\(Z_r = 400\)

\(Z_c = \frac{1}{j\text{wc}}, or \frac{-j}{wc}\)

\(w_C = 500000 \times 2\pi \times 0.001e^{-6}\)

Thus, \[Z_{eq} = Z_r+Z_c = 400 -j318.3\]

For more information, please see Ham Radio School site article called Complex Impedance Part 3: Putting It All Together.

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