Inductance definition: one henry is the inductance that produces a counter electromotive force (emf) of 1 V when the current through the inductor changes at the rate of 1 A per second (E = −L * di/dt).

Introduction / Context:
Inductors oppose changes in current. The quantitative relationship between changing current and the induced counter electromotive force (back emf) is captured by Faraday’s law specialized for inductance: E = −L * di/dt. Understanding the unit “henry” is essential for circuit analysis, filter design, and power electronics where transient behavior matters.

Given Data / Assumptions:

• E denotes induced voltage (volts).
• L denotes inductance (henries).
• di/dt denotes the rate of change of current (amperes per second).
• We are using SI units.

Concept / Approach:
By definition, if di/dt = 1 A/s and the induced emf magnitude is 1 V, then L = 1 H. In practical terms, an inductor of 1 H will produce 1 V of back emf when its current ramps at 1 A every second. This simple proportionality underpins how inductors smooth current (low di/dt for given voltage) or, conversely, how a given ramp demands a specific voltage across the inductor.

Step-by-Step Solution:
Start with E = −L * di/dt.Set E = 1 V, di/dt = 1 A/s.Solve for L: L = 1 V / (1 A/s) = 1 H.Therefore, the statement of one henry matches option B.

Verification / Alternative check:
Check dimensional consistency: volt = henry * ampere/second → henry = volt * second / ampere, which is the SI unit definition for inductance.

Why Other Options Are Wrong:
Option A speaks about “reducing current to 1 A,” not a rate of change. Option C incorrectly ties inductance to frequency change directly. Option D is not a unit definition; turns and current relate to magnetomotive force, not the unit henry alone. “None” is wrong because B states the correct definition.

Common Pitfalls:
Ignoring the negative sign (which only indicates polarity opposing current change); conflating stored energy (0.5 * L * I^2) with the unit definition.

Final Answer:
the amount of inductance required for generating 1 V of counter emf when the current changes at the rate of 1 A per second