Subelement B: Electrical Math— Topic 16: Impedance Networks-1
Question 3-16B4
Element 3 (GROL)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?
Explanation
The impedance of a series circuit in rectangular coordinates is expressed as Z = R + jX, where R is the resistance and X is the reactance. For an inductor, the reactance (XL) is positive, contributing a +jXL term.
First, calculate the inductive reactance (XL) using the formula XL = 2πfL:
* R = 200 Ω
* L = 1.0 mH = 0.001 H
* f = 30 kHz = 30,000 Hz
XL = 2 * π * (30,000 Hz) * (0.001 H)
XL ≈ 188.5 Ω
Since the resistor and inductor are in series, the total impedance is Z = R + jXL.
Therefore, Z = 200 + j188.5 Ω.
Option B, 200 + j188, is the closest match to this calculation. Options A and D are incorrect because an inductor adds a positive imaginary (inductive) reactance, not a negative one. Options C and D incorrectly swap the real (resistance) and imaginary (reactance) components.
Related Questions
3-16B2 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?3-16B3 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?3-16B5 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?3-16B6 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?3-17B1 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.