Capacitor Charging Time Calculator (RC Time Constant)

RC Time Constant Guide

What the RC Time Constant Is

When a capacitor charges through a resistor (or discharges), the voltage doesn't change linearly — it follows an exponential curve. The time constant τ (tau) = R × C. Where: R = resistance in ohms. C = capacitance in farads. τ = time in seconds. Example: 10kΩ resistor + 100µF capacitor. τ = 10,000 × 0.0001 = 1 second. Charging from 0V toward V_supply: V(t) = V_supply × (1 - e^(-t/τ)). Discharging from V_initial toward 0: V(t) = V_initial × e^(-t/τ). Key benchmarks: 1τ: 63.2% charged. 2τ: 86.5%.

Practical Time Constants

Component combinations and their τ: 1kΩ + 1nF: τ = 1µs. Radio frequency, signal filtering. 10kΩ + 1µF: τ = 10ms. Audio coupling, simple debouncing. 100kΩ + 10µF: τ = 1s. LED fade circuits, simple timers. 1MΩ + 100µF: τ = 100s. Long-period timers, slow envelope generators. 10MΩ + 1F: τ = 10,000,000s = ~115 days. Super-capacitor backup applications. Time to 'fully charge' (5τ): nanoseconds for RF circuits. Tens of microseconds for switching power supplies. Tens of milliseconds for audio circuits.

Filter Behaviour

RC circuits naturally filter signals. Low-pass filter: cutoff frequency f_c = 1/(2π·R·C). Frequencies below f_c pass through. Frequencies above are attenuated. High-pass filter: same formula. Frequencies above f_c pass. Below are attenuated. Audio applications: high-pass to remove DC offset, low-frequency rumble. Low-pass to smooth digital PWM into analog signals. Power supply applications: large bulk capacitors (10,000µF+) smooth rectified mains. Time constant in seconds — slow ripple voltage.

Practical Applications

Switch debouncing: mechanical switches bounce 1-10ms when pressed. RC circuit (10kΩ + 0.1µF, τ=1ms) plus Schmitt trigger eliminates bouncing. Camera flash: large electrolytic capacitor (200-500µF) charges through low resistance, then discharges through flash tube in <1ms. Coupling: AC signals pass through, DC blocked. Used in audio amplifiers between stages. Timers: 555 timer chip uses RC for time delays — calculator gives the time constant. 1MΩ + 1µF = 1 second delay typical. Camera shutter tim