Counter-emf law for inductors: The magnitude of induced voltage across an inductor depends on what parameter(s), holding all else the same?

Introduction / Context:
Inductors generate a counter electromotive force (emf) whenever the current through them changes. This phenomenon is central to understanding switching transients, snubbers, and the behavior of RL circuits under step inputs. The quantitative relationship is captured by the inductor voltage equation.

Given Data / Assumptions:

• Ideal inductor model is used.
• Current varies with time, producing an induced voltage.
• We compare proportionalities while other variables are held constant.

Concept / Approach:
The governing relation is v_L = L * di/dt. The induced voltage increases with larger inductance L and with faster current changes di/dt. For a fixed current change occurring over a shorter time, di/dt increases, producing a larger voltage spike. Conversely, a small inductance or slow current change produces a smaller induced voltage.

Step-by-Step Solution:
Write the inductor law: v_L = L * di/dt.Hold di/dt constant → v_L ∝ L (directly proportional to inductance).Hold L constant → v_L ∝ di/dt (larger change in current per unit time gives larger voltage).Therefore, the correct proportionality with respect to L alone is “directly proportional to the inductance in henrys.”

Verification / Alternative check:
Observe switching in a lab: doubling inductance in a given RL step raises the induced voltage during rapid transients proportionally, matching v_L = L * di/dt.

Why Other Options Are Wrong:
Inversely proportional to the change in current: conflicts with the di/dt term.Directly proportional to change in time: for a fixed current change, longer time lowers di/dt and thus reduces v_L.Inversely proportional to inductance: contradicts v_L ∝ L.

Common Pitfalls:
Confusing di/dt with Δi or Δt independently; always consider the ratio. Also, note the sign of v_L follows Lenz’s law, opposing the change in current.

Final Answer:
directly proportional to the inductance in henrys