Principle of mutual induction — key dependency: Mutual induction between two coils primarily depends on which factor in operation?

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:

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