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Inductors
11 questions By Tony R. Kuphaldt
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Question 1 of 11
∫f(x) dx Calculus alert!
A 5 H inductor is subjected to an electric current that changes at a rate of 4.5 amps per second. How much voltage will be dropped by the inductor?Reveal answerThis inductor will drop 22.5 volts.
Notes:Don’t give your students the equation with which to perform this calculation! Let them find it on their own. The [di/dt] notation may be foreign to students lacking a strong mathematical background, but don’t let this be an obstacle to learning! Rather, use this as a way to introduce those students to the concept of rates of change, and to the calculus concept of the derivative.
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Question 2 of 11
∫f(x) dx Calculus alert!
Suppose an inductor is connected to a variable current source, where the current is steadily increased at a rate of 1.5 amps per second. How much voltage will the 4 Henry inductor drop, and what will be the polarity of that drop? Remember, the direction of the arrow in a current source symbol points in the direction of conventional flow, not electron flow!
In real life, an inductor will not drop the exact same amount of voltage that you will calculate here. Determine if the real voltage drop across such an inductor would be greater or less than predicted, and explain why.
Reveal answer
In real life, through, the inductor would drop more than 6 volts, due to winding resistance.
Follow-up question: research the typical winding resistance of a 4 henry inductor.
Notes:Ahhh, the controversy of conventional versus electron flow. The existence of two contradicting conventions for denoting direction of electric current irritates me to no end, especially when the one upon which almost all electronic device symbolism is based on is actually incorrect with regard to charge flow through metallic conductors (the majority case in electric circuits)! Your students will surely encounter both “conventional” and “electron” flow in their careers, so be sure to introduce them to both conventions.
Discuss with your students the consequences of winding resistance in real inductors. Is it significant? Work together with your students to calculate how much extra voltage would be dropped across the inductor, based on their research on the typical winding resistance of a 4 henry inductor (ask them where they obtained the information!), given a [di/dt] rate of 1.5 amps per second.
Ask your students if they think it might be possible to create an inductor with no “stray” resistance at all to interfere with perfect, theoretical inductor behavior. What would be required to make the “perfect” inductor?
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Question 3 of 11
Two 5 H inductors connected in series are subjected to an electric current that changes at a rate of 4.5 amps per second. How much voltage will be dropped across the series combination?
Now suppose that two 5 H inductors connected in parallel are subjected to the same total applied current (changing at a rate of 4.5 amps per second). How much voltage will be dropped by these inductors? Hint: the total current is divided evenly between the two inductors.
Reveal answerSeries connection: 45 volts total. Parallel connection: 11.25 volts total.
Follow-up question: what do these figures indicate about the nature of series-connected and parallel connected inductors? In other words, what single inductor value is equivalent to two series-connected 5 H inductors, and what single inductor value is equivalent to two parallel-connected 5 H inductors?
Notes:If your students are having difficulty answering the follow-up question in the Answer, ask them to compare these voltage figures (45 V and 11.25 V) against the voltage that would be dropped by just one of the 5 H inductors under the same condition (an applied current changing at a rate of 4.5 amps per second).
It is, of course, important that students know how series-connected and parallel connected inductors behave. However, this is typically a process of rote memorization for students rather than true understanding. With this question, the goal is to have students come to a realization of inductor connections based on their understanding of series and parallel voltages and currents.
