Calculate Time Constant (τ), Cutoff Frequency & Current Growth/Decay Times
💡 Formulas: τ = L / R | f_c = R / (2π × L) | i(t) = V/R × (1 - e^(-t/τ))
τ = L / R | f_c = R / (2π × L)
📖 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)
📊 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
📌 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
High-Pass Filters: Pass high frequencies, block low frequencies
Power Supply Chokes: Smoothing and filtering in power supplies
Motor Control: Inductor current control in DC motors
Relay and Solenoid Drivers: Current rise/decay time calculation
❓ Frequently Asked Questions
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. τ = L / R.
How long for current to reach steady state? ▼
5τ (99.3% of final current). For practical purposes, 5τ is considered steady state.
What is the cutoff frequency of an RL circuit? ▼
f_c = R / (2π × L). The frequency where output drops to 70.7% of input.
What happens at t = τ? ▼
Current reaches 63.2% of final value. Inductor voltage drops to 36.8% of initial.