Steady state: I_max = V₀ / R (inductor acts as short circuit)
In an RL circuit, the inductor opposes current changes. When voltage is applied, current rises exponentially. When removed, current decays exponentially. The time constant τ = L/R determines the speed. After 5τ, steady state is reached where the inductor acts like a short circuit (zero DC resistance).
⚠At t=0, inductor acts like an open circuit (maximum voltage across it, zero current initially). At steady state (5τ), inductor acts like a short circuit. The stored magnetic energy is ½LI².
Understanding RL Circuits
An RL circuit consists of a resistor and inductor in series. When power is applied, the inductor initially opposes current flow, causing a gradual current rise. The time constant τ = L/R governs how fast the current changes. RL circuits are fundamental to understanding filter behavior and inductive loads.
Current Rise
I(t) = V₀/R × (1-e^(-t/τ)). Fast initial rise, approaches I_max = V₀/R. Time constant τ = L/R.
Current Decay
I(t) = I₀ × e^(-t/τ). Fast initial drop. Voltage reverses across inductor (flyback). Always use protection diodes.
Filter Cutoff
RL low-pass: fc = R/(2πL). RL high-pass: fc = R/(2πL) (differentiator). Above fc: signal passes. Below: attenuated.
Key Percentages
1τ = 63.2%, 2τ = 86.5%, 3τ = 95%, 4τ = 98.2%, 5τ = 99.3%. Time to X%: t = -τ × ln(1-X/100).
Teaching Example: L=10mH, R=100Ω, V₀=5V.
τ = 0.01/100 = 0.0001s = 100μs. I_max = 5/100 = 50mA.
At t=100μs (1τ): I = 50mA × 0.632 = 31.6mA. At t=500μs (5τ): I = 49.7mA (steady state).
τ = L/R (seconds). Time for inductor current to reach 63.2% of final value. 5τ = steady state (99.3%).
RL vs RC difference?▼
RC: τ=RC (capacitor voltage). RL: τ=L/R (inductor current). Both exponential, same percentages. RC stores in electric field, RL in magnetic.
What is steady state in RL?▼
After 5τ, current reaches 99.3% of I_max = V₀/R. The inductor acts like a short circuit (wire) to DC. All voltage is across the resistor.
Why does RL circuit spark?▼
V = L × dI/dt. When current is interrupted, dI/dt is large, creating high voltage. This causes arcing across switches. Use a flyback diode for protection.
Free online calculators and tools covering mathematics, unit conversion, text processing, and daily life. Accurate, fast, mobile-friendly, and completely free to use.