Difficulty: Easy
Correct Answer: directly proportional to the number of turns squared
Explanation:
Introduction / Context:Inductance quantifies a coil’s ability to store magnetic energy for a given current. Designers adjust turns, core materials, and geometry to achieve target inductance values for filters, chokes, and resonant circuits. Knowing the correct proportionalities prevents costly trial-and-error.
Given Data / Assumptions:
Concept / Approach:A widely used approximate relation is L ∝ μ * N^2 * A / l, where μ is permeability, N is turns count, A is cross-sectional area, and l is magnetic path length. Thus, inductance grows with permeability, with area, and with the square of the turns, and it decreases with longer magnetic paths.
Step-by-Step Solution:Start from the proportionality: L ∝ μ * N^2 * A / l.Analyze parameter effects: increasing N strongly raises L because of the N^2 factor.Increasing length l lowers L; increasing area A raises L; higher μ raises L.Therefore, the statement “directly proportional to the number of turns squared” is the most accurate among the options.
Verification / Alternative check:Doubling turns approximately quadruples inductance if μ, A, and l remain constant. This square-law behavior is well established in inductor design references and verified in practical winding experiments.
Why Other Options Are Wrong:Direct proportionality to length is incorrect; L falls as length increases.
Inverse proportionality to area and to permeability are both wrong; L increases with A and μ.
Independence from core material is false; μ of the core is a dominant factor.
Common Pitfalls:Assuming L increases linearly with turns; the correct dependence is N^2 for tightly coupled coils.
Final Answer:directly proportional to the number of turns squared
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