Inductance unit check in circuit theory: If an inductor experiences a current change of 1 ampere per second and the induced voltage across it is 1 volt, this corresponds to which standard unit value?

Introduction / Context:When studying inductors in basic circuit theory, a key relationship is the voltage induced across an inductor due to a changing current. Identifying the correct unit from the voltage–current rate-of-change relationship helps cement the definition of the henry, the SI unit of inductance.

Given Data / Assumptions:

• Induced voltage across the inductor: v = 1 V.
• Rate of change of current: di/dt = 1 A/s.
• Standard inductor behavior with linear inductance and no core saturation.

Concept / Approach:

The governing formula for an ideal inductor is v = L * di/dt. Rearranging gives L = v / (di/dt). Substituting the provided values immediately yields the inductance in henrys. The henry is defined so that 1 H produces 1 V when current changes at 1 A/s.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional analysis confirms consistency: volt = henry * ampere/second → henry = volt / (ampere/second) = voltsecond/ampere, which is the SI definition of 1 H.

Why Other Options Are Wrong:

• a lenz: Not a unit; Lenz’s law states polarity of induced emf.
• an ohm: Unit of resistance; relates voltage and current directly (V = IR), not di/dt.
• a farad: Unit of capacitance defined by i = C * dv/dt, not v = L * di/dt.
• a weber: Unit of magnetic flux; not the unit for inductance.

Common Pitfalls:

• Confusing the inductor formula with the capacitor formula and swapping roles of current and voltage derivatives.
• Mixing up henry with weber or tesla; those quantify flux and flux density, not inductance itself.

Final Answer:

a henry