RL circuits — When an inductance value (in henry) is divided by the circuit’s resistance (in ohms), what engineering quantity do you obtain for a first-order RL network?

Introduction:The ratio of inductance to resistance, written as L / R, is a cornerstone parameter for first-order RL circuits. It sets how quickly current builds up or decays when a step voltage is applied or removed, directly determining transient speed in power electronics, filters, and sensor interfaces.

Given Data / Assumptions:

• First-order series RL network with inductance L (henry) and resistance R (ohm).
• Excited by a step or switched DC voltage source.
• Linear, time-invariant components; no saturation or temperature drift considered.

Concept / Approach:

The natural response of an RL circuit follows an exponential with time constant tau = L / R. This constant determines how fast current approaches its final steady value. After approximately 5 * tau, current is essentially settled. The same tau governs decay after de-energizing the inductor.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional analysis: 1 H = 1 V·s/A and 1 Ω = 1 V/A, so H/Ω = (V·s/A)/(V/A) = s, confirming a time measure. Simulation or oscilloscope traces of RL steps validate that 63.2% of the final current is reached at t = tau.

Why Other Options Are Wrong:

• counter emf value: That is an instantaneous induced voltage, not a constant and not L/R.
• induced voltage amplitude: Depends on di/dt and turns; not equal to L/R.
• quality factor: Q involves reactance/resistance at a frequency; not simply L/R in seconds.
• phase angle at resonance: Resonance pertains to RLC; an RL alone does not resonate.

Common Pitfalls:

• Confusing L/R (seconds) with X_L = 2 * pi * f * L (ohms).
• Assuming tau gives exact settling time; it only characterizes exponential rate (use multiples of tau for design).

Final Answer:

rise or decay time constant