RL transient behavior: in a first-order inductive (RL) circuit, does the time constant depend on the circuit resistance?

Introduction / Context:Time constant governs how quickly currents and voltages rise or decay during switching events in first-order circuits. For RL networks, the time constant directly affects relay delays, inrush current, and filter settling. This question asks whether resistance influences that time constant.

Given Data / Assumptions:

• Series RL driven by a step input.
• Inductor L and total effective series resistance R (including source and winding resistance).
• Linear operation without core saturation.

Concept / Approach:The RL time constant is τ = L / R (seconds). Larger resistance speeds up decay (smaller τ), while larger inductance slows it down (larger τ). This emerges from the differential equation: L * di/dt + R * i = V_step, whose homogeneous solution is i(t) = I_final * (1 − exp(−t/τ)) for a rise or i(t) = I_initial * exp(−t/τ) for a decay.

Step-by-Step Solution:

Verification / Alternative check:Check limits: as R → 0, τ → ∞ (current changes very slowly); as R → ∞, τ → 0 (current cannot build, response is fast).

Why Other Options Are Wrong:Incorrect or “depends only on inductance”: both ignore the R term that sets the decay rate. Depends only on source voltage: voltage scales final current, not the exponential time constant.

Common Pitfalls:Confusing RL (τ = L/R) with RC (τ = R*C); forgetting that any series resistance adds to R, including winding and source resistances.

Final Answer:Correct