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).
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Athe amount of counter emf required to reduce a current to 1 A
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Bthe amount of inductance required for generating 1 V of counter emf when the current changes at the rate of 1 A per second
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Cthe amount of inductance required to change the frequency of a current by 1 Hz
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Dthe number of turns of wire in an inductor multiplied by the amount of current flowing through it
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ENone of the above
Answer
Correct 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
Explanation
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