What is a Time Constant?
The time constant (τ) is the time it takes for a circuit to charge or discharge to 63.2% of its final value. It's a fundamental characteristic of RC and RL circuits that determines their response speed.
RC Circuits
- Time constant: τ = R × C
- Used in timing circuits, filters, and coupling circuits
- Larger capacitance = slower response (longer time constant)
- Larger resistance = slower response (longer time constant)
RL Circuits
- Time constant: τ = L / R
- Used in inductive loads, motors, and transformers
- Larger inductance = slower response (longer time constant)
- Larger resistance = faster response (shorter time constant)
Response Times
- After 1τ: 63.2% of final value
- After 3τ: 95% of final value (practical settling time)
- After 5τ: 99.3% of final value (considered steady state)
- Exponential decay/rise follows: V(t) = V₀ × (1 - e^(-t/τ))
Applications
- RC: Timer circuits, low-pass/high-pass filters, flash photography
- RL: Motor startup, relay circuits, inductive switching
- Signal processing: determining bandwidth and frequency response
- Power electronics: snubber circuits and soft-start circuits
Tips
- Use scientific notation for very small values (e.g., 1µF = 1e-6 F)
- Faster response time requires smaller time constant
- Common capacitor values: pF (1e-12), nF (1e-9), µF (1e-6)
- Common inductor values: µH (1e-6), mH (1e-3), H (1)