Principle of mutual induction — key dependency: Mutual induction between two coils primarily depends on which factor in operation?
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Awinding ratios
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Boutput polarities
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Cdc voltage levels
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Dcurrent changes
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Ecore weight only
Answer
Correct Answer: current changes
Explanation
Introduction / Context:Mutual induction is the foundation of transformer action, inductive sensors, and many coupling phenomena in electronics. It concerns how a changing current in one coil produces a changing magnetic flux that links a second coil, thereby inducing a voltage according to Faraday’s law and Lenz’s law.
Given Data / Assumptions:
- Two coils placed such that some flux from one links the other.
- Time-varying current in at least one coil (AC or switched DC).
- Finite coupling coefficient k > 0 determined by geometry and core material.
Concept / Approach:
Induced voltage e_2 in coil 2 is proportional to the time rate of change of the flux linked with it. Since flux linkage from coil 1 is driven by its current, the key operational dependency is on di/dt of the primary (exciting) coil. Faster changes (higher frequency or sharp switching) yield larger induced voltages; constant DC (no change) produces no sustained induced voltage after transients.
Step-by-Step Solution:
Start with Faraday relation: induced emf ∝ dΦ/dt.Flux Φ from coil 1 is proportional to i_1 (in linear operation). Therefore, dΦ/dt ∝ di_1/dt.Thus, mutual induction depends directly on current changes (di/dt) in the exciting coil.Higher frequency or rapid switching → larger induced voltage for the same current amplitude.Verification / Alternative check:
Experimentally, connect a scope to the secondary while stepping the primary current: only during transitions (turn-on/turn-off) does the secondary show a pulse. With sinusoidal excitation, the induced voltage follows frequency and amplitude, confirming dependence on di/dt.
Why Other Options Are Wrong:
- Winding ratios affect voltage scaling but do not create induction without changing current.
- Output polarities result from winding orientation and dot convention, not the presence of induction itself.
- DC voltage levels alone produce no sustained induction if current is constant.
- Core weight is not the determining factor; material and geometry affect coupling, but induction requires change in current.
Common Pitfalls:
- Expecting continuous induced voltage from steady DC; only transients induce until currents stabilize.
- Confusing mutual inductance value (a parameter) with the operational condition (di/dt) required for induced emf.
Final Answer:
current changes