or
Subelement B
Electrical Math
Section 17
Impedance Networks-2
What is the impedance of a network composed of a 100-picofarad capacitor in parallel with a 4000-ohm resistor, at 500 KHz? Specify your answer in polar coordinates.
• 2490 ohms, /51.5 degrees
• 4000 ohms, /38.5 degrees
• 5112 ohms, /-38.5 degrees
2490 ohms, /-51.5 degrees

What is the impedance of a network composed of a
100-picofarad capacitor in parallel with a
4000-ohm resistor, at
500 KHz?

2490 ohms, /-51.5 degrees

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

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In polar coordinates, what is the impedance of a network composed of a 100-ohm-reactance inductor in series with a 100-ohm resistor?
• 121 ohms, /35 degrees
141 ohms, /45 degrees
• 161 ohms, /55 degrees
• 181 ohms, /65 degrees

In polar coordinates, what is the impedance of a network composed of a
100-ohm-reactance inductor in series with a
100-ohm resistor?

141 ohms, /45 degrees

From wp2ahg:

\begin{align} Z &= \sqrt{(R^2 + (XL- XC)^2)}\\ &= \sqrt{(100^2\text{ ohms} + (100\text{ ohms} - 0\text{ ohms})^2)}\\ &=\sqrt{(10,000\text{ ohms} + 10,000\text{ ohms}}\\ &=\sqrt{(20,000\text{ ohms}}\\ &= 141\text{ ohms}\\ \\ \end{align}

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In polar coordinates, what is the impedance of a network composed of a 400-ohm-reactance capacitor in series with a 300-ohm resistor?
• 240 ohms, /36.9 degrees
• 240 ohms, /-36.9 degrees
500 ohms, /-53.1 degrees
• 500 ohms, /53.1 degrees

In polar coordinates, what is the impedance of a network composed of a
400-ohm-reactance capacitor in series with a
300-ohm resistor?

500 ohms, /-53.1 degrees

From wp2ahg:

(Xl - XR) tells you if it's positive or negative.
(0 ohms - 300 ohms) = -300 ohms, so it's negative.

\begin{align} Z &= \sqrt{(R^2 + (XL- XC)^2)}\\ &= \sqrt{(300^2\text{ ohms} + (400\text{ ohms} - 0\text{ ohms})^2)}\\ &=\sqrt{(900\text{ ohms} + 1,600\text{ ohms}}\\ &=\sqrt{(2,500\text{ ohms}}\\ &= 500\text{ ohms}\\ \\ \end{align}

So, the answer is 500 ohms, and negative.

Answer C is the only 500 ohm/negative answer, so that's the right choice.

You can calculate the degrees if you want, but it's not necessary for answering this question.

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In polar coordinates, what is the impedance of a network composed of a 300-ohm-reactance capacitor, a 600-ohm-reactance inductor, and a 400-ohm resistor, all connected in series?
500 ohms, /37 degrees
• 400 ohms, /27 degrees
• 300 ohms, /17 degrees
• 200 ohms, /10 degrees

In polar coordinates, what is the impedance of a network composed of a
300-ohm-reactance capacitor, a
600-ohm-reactance inductor, and a
400-ohm resistor,
all connected in series?

500 ohms, /37 degrees

From wp2ahg:

\begin{align} Z &= \sqrt{(R^2 + (XL- XC)^2)}\\ &= \sqrt{(400^2\text{ ohms} + (600\text{ ohms} - 300\text{ ohms})^2)}\\ &=\sqrt{(160,000\text{ ohms} + 90,000\text{ ohms}}\\ &=\sqrt{(250,000\text{ ohms}}\\ &= 500\text{ ohms}\\ \\ \end{align}

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In polar coordinates, what is the impedance of a network comprised of a 400-ohm-reactance inductor in parallel with a 300-ohm resistor?
• 240 ohms, /-36.9 degrees
240 ohms, /36.9 degrees
• 500 ohms, /53.1 degrees
• 500 ohms, /-53.1 degrees

In polar coordinates, what is the impedance of a network comprised of a
400-ohm-reactance inductor in parallel with a
300-ohm resistor?

240 ohms, /36.9 degrees

From wp2ahg:

Total impedance for a parallel RL circuit is:
${\text{Impedance}=\frac{\text{Resistance x Reactance}}{\sqrt{\text{Resistance^2} \ + \text{Reactance^2}}\\}}$

${\text{Impedance}=\frac{300 * 400}{\sqrt{300^2 \ + 400^2}\\}}$

${\text{Impedance}=\frac{300 * 400}{\sqrt{90,000 \ + 160,000}\\}}$

${\text{Impedance}=\frac{120,000}{\sqrt{250,000}\\}}$

${\text{Impedance}=\frac{120,000}{{500}\\}}$

${\text{Impedance}={240\text{ ohms}\\}}$

Phase Angle for a parallel RL circuit is
= Degrees(arctan(Reactance / Resistance))°

= Degrees(arctan(300/400))°
= Degrees(arctan(0.75))°
= Degrees(0.64)°
= 36.9° degrees

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Using the polar coordinate system, what visual representation would you get of a voltage in a sinewave circuit?
• To show the reactance which is present.
• To graphically represent the AC and DC component.
• To display the data on an XY chart.