⏱️ RC Time Constant

Formulas

τ = R × C
Charge: V(t) = Vcc × (1 − e^−t/τ)
Discharge: V(t) = V₀ × e^−t/τ
Time to V: t = −τ × ln(1 − V/Vcc)

Multiples of τ

• 1τ — 63.2% of Vcc (1 time constant)
• 2τ — 86.5%
• 3τ — 95.0% — often considered "charged"
• 4τ — 98.2%
• 5τ — 99.3% — fully charged in practice

Common applications

• Debounce — RC + Schmitt trigger on button input
• Delay circuit — charge cap to trigger threshold
• Low-pass filter — fc = 1 / (2π × R × C)
• Integrator — op-amp with RC in feedback
• Reset circuit — RC on microcontroller RESET pin
• 555 timer — charging time sets frequency/pulse

Practical notes

• Capacitor ESR and leakage affect actual charge time
• Load resistance changes effective R — use a buffer (op-amp) if needed
• Electrolytic caps: observe polarity
• Ceramic caps (X5R/X7R) have less voltage-dependent capacitance variation than Y5V
• For precision timing, use film capacitors