RC Time Constant and Capacitor Charging

When a capacitor charges through a resistor, it doesn't fill instantly. The charge follows an exponential curve defined by the time constant τ = R × C (in seconds, when R is in ohms and C in farads). After one time constant, the capacitor reaches 63.2% of the supply voltage. After 5τ, it's considered fully charged (99.3%).

The Formulas

• Time constant: τ = R × C
• Voltage at time t: V(t) = V_supply × (1 − e^(−t/τ))
• Time to reach voltage V: t = −τ × ln(1 − V/V_supply)
• Charge and discharge are symmetric (discharge: V(t) = V_initial × e^(−t/τ))

How to Use This Calculator

Enter the resistance (R), capacitance (C), and supply voltage. The calculator outputs the time constant, time to reach various charge levels (50%, 63.2%, 90%, 99%), and the full charge/discharge curve.

Practical Examples

Example 1: R = 10kΩ, C = 100µF. τ = 10,000 × 0.0001 = 1 second. Full charge in ~5 seconds.

Example 2: R = 1MΩ, C = 1µF. τ = 1 second (same — many combinations give the same τ).

Example 3: Camera flash with C = 1,000µF, R = 500Ω. τ = 0.5s. Recharge in ~2.5 seconds.

Applications

RC time constants are used in timer circuits (555 timers), signal filtering, audio crossovers, debouncing switches, and setting reset delay times in microcontroller power-on reset circuits.