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Impedance
19 questions By Tony R. Kuphaldt
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Question 7 of 19
Express the impedance (Z) in both polar and rectangular forms for each of the following components:
- A resistor with 500 Ω of resistance
- An inductor with 1.2 kΩ of reactance
- A capacitor with 950 Ω of reactance
- A resistor with 22 kΩ of resistance
- A capacitor with 50 kΩ of reactance
- An inductor with 133 Ω of reactance
Reveal answer- A resistor with 500 Ω of resistance: 500 Ω ∠ 0o or 500 j0 Ω
- An inductor with 1.2 kΩ of reactance: 1.2 kΩ ∠ 90o or 0 j1.2k Ω
- A capacitor with 950 Ω of reactance: 950 Ω ∠ -90o or 0 - j950 Ω
- A resistor with 22 kΩ of resistance: 22 kΩ ∠ 0o or 22k j0 Ω
- A capacitor with 50 kΩ of reactance: 50 kΩ ∠ -90o or 0 - j50k Ω
- An inductor with 133 Ω of reactance: 133 Ω ∠ 90o or 0 j133 Ω
Follow-up question: what would the phasors look like for resistive, inductive, and capacitive impedances?
Notes:In your discussion with students, emphasize the consistent nature of phase angles for impedances of “pure” components.
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Question 8 of 19
Real inductors and capacitors are never purely reactive. There will inevitably be some resistance intrinsic to these devices as well.
Suppose an inductor has 57 Ω of winding resistance, and 1500 Ω of reactance at a particular frequency. How would this combination be expressed as a single impedance? State your answer in both polar and rectangular forms.
Reveal answerZL = 1501 Ω ∠ 87.8o = 57 + j1500 Ω
Notes:Mention to your students that “real” components such as this may be modeled in a diagram as a combination of two “pure” components, in this case a resistor and an inductor. Discuss with them the benefits of “modeling” component characteristics in this manner, since it is a very common practice in engineering.
This is a very important concept to understand: that reactive components are never purely reactive. Parasitic resistance is impossible to avoid short of using superconductors. Even then, inductors are bound to have some parasitic capacitance, and capacitors are bound to have some parasitic inductance!
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Question 9 of 19
Not only do reactive components unavoidably possess some parasitic (“stray”) resistance, but they also exhibit parasitic reactance of the opposite kind. For instance, inductors are bound to have a small amount of capacitance built-in, and capacitors are bound to have a small amount of inductance built-in. These effects are not intentional, but they exist anyway.
Describe how a small amount of capacitance comes to exist within an inductor, and how a small amount of inductance comes to exist within a capacitor. Explain what it is about the construction of these two reactive components that allows the existence of “opposite” characteristics.
Reveal answerCapacitance exists any time there are two conductors separated by an insulating medium. Inductance exists any time a magnetic field is permitted to exist around a current-carrying conductor. Look for each of these conditions within the respective structures of inductors and capacitors to determine where the parasitic effects originate.
Notes:Once students have identified the mechanisms of parasitic reactances, challenge them with inventing means of minimizing these effects. This is an especially practical exercise for understanding parasitic inductance in capacitors, which is very undesirable in decoupling capacitors used to stabilize power supply voltages near integrated circuit “chips” on printed circuit boards. Fortunately, most of the stray inductance in a decoupling capacitor is due to how it’s mounted to the board, rather than anything within the structure of the capacitor itself.
