Inductance units and definitions: When a current changes at a rate of 1 ampere per second and induces 1 volt across a coil, what is the unit of inductance defined by this relationship?

Introduction / Context:
Inductance quantifies how effectively a coil resists changes in current by developing an induced voltage. Recognizing the definition tied to basic units allows quick sanity checks in transient circuit analysis and in sizing inductors for filters or power converters.

Given Data / Assumptions:

• The induced voltage v across an inductor is v = L * di/dt.
• Given di/dt = 1 A/s results in v = 1 V.
• SI base units are used throughout.

Concept / Approach:
By definition, an inductance of 1 henry produces 1 volt of induced EMF when the current through it changes at 1 ampere per second. The equation v = L * di/dt directly encodes this. The henry (H) is the SI unit of inductance; alternative options list unrelated units (ohm for resistance, farad for capacitance) or a nonstandard term that does not exist in SI (lenz).

Step-by-Step Solution:

Verification / Alternative check:
Dimensional analysis: [L] = V / (A/s) = V * s / A, which is the dimension of the henry.

Why Other Options Are Wrong:

• Ohm: Unit of resistance (V/A).
• Farad: Unit of capacitance (C/V or s/Ω).
• “Lenz”: Not an SI unit; Lenz's law describes polarity of induced EMF, not a unit.

Common Pitfalls:
Confusing the roles of L, R, and C in differential equations; always tie the unit back to v = L * di/dt.

Final Answer:
a henry