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Inductance
20 questions By Tony R. Kuphaldt
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Question 7 of 20
Inductance is a very important property in many types of electric circuits. Define what “inductance” is, and what causes it.
Reveal answer“inductance” is the capacity of a conductor to store energy in the form of a magnetic field, resulting from an applied current. You may also find a definition of “inductance” stated in terms of opposition to change in applied current over time.
Inductance is caused by the establishment of a magnetic field around a conductor.
Notes:Ask students what unit of measurement inductance is expressed in. Also, ask them if they think the inductance of any given conductor changes with the applied current or stored energy, or if inductance is a quantity independent of particular electrical conditions.
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Question 8 of 20
∫f(x) dx Calculus alert!
If the number of turns of wire in an electromagnet coil is tripled, what happens to the magnitude of the magnetic flux (Φ) generated by it, assuming that none of the other variables change (current through the coil, reluctance of magnetic circuit, etc.)?If the number of turns of wire in an inductor is tripled, what happens to the magnitude of the induced voltage for a given rate of magnetic flux change over time \(\frac{dφ}{dt}\)?
If the number of turns of wire in an inductor is tripled, what happens to the magnitude of its inductance, measured in Henrys? Explain your answer.
Reveal answerIf N triples, then Φ triples, all other factors being equal.
If \(\frac{dφ}{dt}\) triples, then e triples, all other factors being equal.
If N triples, then L increases by a factor of nine, all other factors being equal.
Notes:This question presents an interesting problem in qualitative mathematics. It is closely related to the “chain rule” in calculus, where one function y = f(x) is embedded within another function z = f(y), such that \(\frac{dz}{dy}\)\(\frac{dy}{dx}\) = \(\frac{dz}{dx}\). The purpose of this exercise is for students to gain a conceptual grasp of why inductance does not vary linearly with changes in N.
Of course, students can obtain the same (third) answer just by looking at the inductance formula (in terms of N, μ, A, and l), without all the conceptual work. It would be good, in fact, if a student happens to derive the same answer by inspection of this formula, just to add variety to the discussion. But the real purpose of this question, again, is a conceptual understanding of that formula.
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Question 9 of 20
The amount of inductance inherent in a wire coil may be calculated by the following equation:
L = N2 A μ lWhere,
L = Inductance in Henrys
N = Number of wire “turns” wrapped around the core
μ = Permeability of core material (absolute, not relative)
A = Core area, in square meters
l = Length of core, in meters
Calculate how many turns of wire must be wrapped around a hollow, non-magnetic (air) core 2 cm in diameter and 10 cm in length in order to create an inductance of 22 mH. You may use the permeability of free space (μ0) for the μ value of the air core.
Next, calculate the required number of turns to produce the same inductance with a solid iron core of the same dimensions, assuming that the iron has a relative permeability (μr) of 4000.
Finally, knowing that the formula for the area of a circle is πr2, re-write the inductance equation so as to accept a value for inductor radius rather than inductor area. In other words, substitute radius (r) for area (A) in this equation in such a way that it still provides an accurate figure for inductance.
Reveal answerApproximately 2360 turns of wire for the air core, and approximately 37 turns of wire for the iron core.
New inductance equation:
L = πN2 r2 μ lNotes:This problem is first and foremost an algebraic manipulation exercise: solving for N given the values of the other variables. Students should be able to research the value of μ0 quite easily, being a well-defined physical constant.
Note that in this equation, the Greek letter “mu” (μ) is not a metric prefix, but rather an actual variable! This confuses many students, who are used to interpreting μ as the metric prefix “micro” \(\frac{1}{1,000,000}\).
Note also how the re-written equation puts pi (π) ahead of all the variables in the numerator of the fraction. This is not absolutely necessary, but it is conventional to write constants before variables. Do not be surprised if some students ask about this, as their answers probably looked like this:
L = N2 πr2 μ l
