How long for current to reach steady state?

5τ (99.3% of final current). For practical purposes, 5τ is considered steady state.

Low-pass vs high-pass RL filter?

Low-pass: output across inductor (passes low frequencies). High-pass: output across resistor (passes high frequencies).

RL Time Constant Calculator | Inductor Resistor

📖 RL Time Constant Calculator

The RL time constant (τ) is the time required for the current in an inductor-resistor circuit to reach approximately 63.2% of its final value. It is given by the ratio of inductance (L) to resistance (R). This calculator computes the time constant, cutoff frequency, and current at specific time intervals. Essential for inductor filter design, power supply circuits, and motor control.

📐 RL Circuit Formulas

Time Constant: τ = L / R (seconds)
Cutoff Frequency: f_c = R / (2π × L) (Hz)
Current Growth: i(t) = V/R × (1 - e^(-t/τ))
Current Decay: i(t) = I0 × e^(-t/τ)

Where:
L = Inductance (H) R = Resistance (Ω)
τ = Time Constant (s) f_c = Cutoff Frequency (Hz)
V = Applied Voltage I0 = Initial Current

📊 RL Time Constant Reference

RL Combination	τ (seconds)	f_c (Hz)	Application
10Ω / 10mH	0.001	159	Power supply filtering
100Ω / 10mH	0.0001	1591	High frequency filters
100Ω / 100mH	0.001	159	Audio filtering
1kΩ / 100mH	0.0001	1591	Signal processing
10Ω / 100mH	0.01	15.9	Low frequency filters
100Ω / 1H	0.01	15.9	Power inductor circuits

📌 Current Growth/Decay Percentages

1τ (63.2%): Current reaches 63.2% of final value
2τ (86.5%): Current reaches 86.5% of final value
3τ (95.0%): Current reaches 95.0% of final value
4τ (98.2%): Current reaches 98.2% of final value
5τ (99.3%): Considered steady state

💡 Applications of RL Circuits

Low-Pass Filters: Pass low frequencies, block high frequencies (output across inductor)
High-Pass Filters: Pass high frequencies, block low frequencies (output across resistor)
Power Supply Chokes: Smoothing and filtering in power supplies
Motor Control: Inductor current control in DC motors
Transformer Circuits: Inductance in transformer windings
Relay and Solenoid Drivers: Current rise/decay time calculation

❓ Frequently Asked Questions (FAQ)

❓ What is the RL time constant? ▼

The RL time constant (τ) is the time required for the current to reach 63.2% of its final value in an inductor-resistor circuit. It is calculated as τ = L / R, where L is in henries and R is in ohms.

❓ How long does it take for current to reach steady state in an RL circuit? ▼

Current is considered to reach steady state after 5 time constants (5τ), reaching about 99.3% of the final current. For practical purposes, 5τ is used.

❓ What is the cutoff frequency of an RL circuit? ▼

The cutoff frequency (f_c) is the frequency at which the output voltage drops to 70.7% of the input voltage. It is calculated as f_c = R / (2π × L).

❓ What is the difference between low-pass and high-pass RL filters? ▼

Low-pass RL filters pass low frequencies and attenuate high frequencies (output across inductor). High-pass RL filters pass high frequencies and attenuate low frequencies (output across resistor).

❓ What happens at t = τ in an RL circuit? ▼

At t = τ, the current reaches 63.2% of its final value. The voltage across the inductor drops to 36.8% of its initial value.

❓ What is the unit of time constant in RL circuits? ▼

The time constant is measured in seconds (s). With L in henries (H) and R in ohms (Ω), τ = H / Ω = seconds.