or
Subelement B
Electrical Math
Section 16
Impedance Networks-1
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
• 19 +j20
20 +j19
• 19 -j20

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

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

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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
• 3 +j30
• 3 -j30
30 +j3

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

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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
• 40 -j31400
• 31400 +j40
• 31400 -j40

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

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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
200 + j188
• 188 + j200
• 188 - j200

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

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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?
• 150 - j159
• 150 + j159
159 - j150
• 159 + j150

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.

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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?
• 318 - j400
• 400 + j318
• 318 + j400
400 - j318

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, $Z_{eq} = Z_r+Z_c = 400 -j318.3$