RL Circuit Transient

Key Equations

• • τ = L / R — time constant (seconds)
• • i(t) = (V/R)(1 − e^(−t/τ)) — current build-up
• • ε(t) = V·e^(−t/τ) — inductor back-EMF
• • At t = τ: current reaches 63.2% of final value
• • At t = 5τ: circuit is effectively at steady state (99.3%)
• • Larger L or smaller R → longer τ → slower rise