In series, the resistance is the resistance of the resistor. The reactive part is either positive or negative - in this case, it's an inductor, so positive. There is only one answer with 20 ohms and a positive reactance, 20 + j19.

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.

Last edited by k6yxh. Register to edit

Tags: none

In series, the resistor is simply the resistance give, 30 ohms. The reactance is either positive or negative - in this case it's inductive, so positive. There is only one answer with 30 ohns and a positive reactance - you don't have to do any calculations.

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.

Last edited by k6yxh. Register to edit

Tags: none

From k6yxh: It's a series circuit, so the resistive part is 40 ohms. That leaves two choices. Inductive reactance is always positive, so the only 40 ohm with positive reactance is 40 + j31400

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.

Last edited by k6yxh. Register to edit

Tags: none

In a series circuit, the resistance is the resistance of the resistor. The reactance is either positive or negative. Inductive reactance is always positive. Only one answer has 200 ohms and a positive reactance - you don't have to do any calculations.

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.

Last edited by k6yxh. Register to edit

Tags: none

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?***

\[159 - j150\]

For study purposes: the j imaginary is ALWAYS (+) for inductors and (-) for capacitors

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.

Last edited by justinlb28. Register to edit

Tags: none

In a series circuit, the resistance is the resistance of the resistor. The reactance is either positive or negative - capaitance is always negative. There is only one answer with 400 ohms and a negative reactance.

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.

Last edited by k6yxh. Register to edit

Tags: none