An inductor is in series with a voltage source, a switch, and a resistor. At the instant the switch is first closed (t = 0+), the inductor behaves as which effective element?

Introduction / Context:
Inductors resist changes in current. When a previously unenergized inductor is suddenly connected in series to a source via a switch, the immediate, transient behavior is governed by di/dt limitations. Recognizing the instant-after behavior is critical in transient analysis and in understanding why inductors protect against inrush currents.

Given Data / Assumptions:

• Initial inductor current iL(0−) = 0 A (switch open for a long time beforehand).
• Ideal inductor (no series resistance), ideal switch, and DC source.
• Observation is at t = 0+ (the instant just after closure).

Concept / Approach:
For an inductor, vL = L * di/dt. Current through an inductor cannot change instantaneously; iL(0+) = iL(0−). With iL initially zero, the inductor initially allows no current (iL remains 0 at t = 0+), acting like an open circuit at that instant. Over time, current rises exponentially toward its steady-state value with time constant τ = L / R, and in steady state a DC inductor behaves like a short (neglecting winding resistance).

Step-by-Step Explanation:
Before closing: iL = 0 A (de-energized).At t = 0+: iL cannot jump, so still 0 A.Zero current implies the path is effectively open at that moment.As time progresses, iL increases and the inductor's effective impedance falls toward 0 Ω in DC steady state.

Verification / Alternative check:
Transient solution for RL: i(t) = (V/R) * (1 − e^(−t/τ)). At t = 0, i(0) = 0, confirming no instantaneous current and open-circuit behavior initially.

Why Other Options Are Wrong:

• A short: Describes steady-state DC behavior after a long time, not the instant after switching.
• A resistor: Inductor impedance is frequency-dependent; at the instant of switching it is effectively infinite for DC current.
• A voltage or current source: Those are active elements; the inductor is passive and does not act as an ideal source at t = 0+.

Common Pitfalls:

• Assuming inductors instantly pass current like resistors; they do not.
• Confusing initial and steady-state behaviors of reactive components.

Final Answer:
an open