RL circuit setup and inductor physics

S OPEN R Vs IL L + − vL Switch open → IL = I0 B magnetic flux initial current: I0 IL through wire creates B field IL builds as flux accumulates

V-I relationship

current–voltage law
v = L di/dt
AC / changing I
di/dt ≠ 0
→ v ≠ 0 — voltage appears
DC steady state
di/dt = 0
→ v = 0 — short circuit
Contrast with capacitor: inductor is a short at DC; capacitor is an open at DC.

Time constant intuition — τ = L/R

Why larger R → faster response

Larger R
  • Smaller Ifinal = V/R
  • τ = L/R decreases → settles faster
time
Smaller R
  • Larger Ifinal = V/R
  • τ = L/R increases → settles slower
time

Current curve — IL(t) = Ifinal + (I0 − Ifinal)e−Rt/L

100 Ω
100 mH
5.0 V
0.0 mA
τ = L/R = 1.0 ms
Ifinal = V/R = 50.0 mA

Inductor voltage v_L(t)

De-energizing — the voltage spike

peak spike |v_L(0⁺)| = I₀ × R_arc
50 V
I₀ × R_arc = 50.0 mA × 10 kΩ — can damage or destroy transistors and ICs
I₀ linked — V/R from Panel 4 steady state 50.0 mA
10 kΩ
← 10 Ω (flyback diode) (open switch) 100 kΩ →
L linked — from Panel 4 100 mH
τ_dis = L/R = 0.100 ms

Current decay — I_L(t) = I₀ · e^(−t / τ)

Inductor voltage — polarity reverses (Lenz's law): v_L(t) = −I₀ R · e^(−t / τ)

No flyback diode (your R setting)
Switch arc or open circuit — high R forces a large spike across the switch and any connected IC
—
With flyback diode (R ≈ 1 Ω)
Current recirculates through diode forward path — spike is clamped to a fraction of a volt
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