Calculate charging and discharging times for resistor-capacitor (RC) circuits. Find τ (tau), cutoff frequency, and voltage at any time.
The RC time constant (τ, tau) represents the time it takes for a capacitor to charge to approximately 63.2% of the supply voltage, or discharge to 36.8% of its initial voltage. After 5τ, the capacitor is considered fully charged or discharged (99.3%).
The capacitor voltage at different multiples of τ:
| Time | Charging % | Discharging % |
|---|---|---|
| 1τ | 63.2% | 36.8% |
| 2τ | 86.5% | 13.5% |
| 3τ | 95.0% | 5.0% |
| 4τ | 98.2% | 1.8% |
| 5τ | 99.3% | 0.7% |
An RC circuit acts as a low-pass filter, allowing low frequencies to pass while attenuating high frequencies. The cutoff frequency (fc) is where the signal is reduced to 70.7% (-3dB).
Example: R = 10kΩ, C = 100nF → fc = 1/(2π × 10000 × 0.0000001) ≈ 159 Hz
RC circuits are used in timing applications like delay circuits, debouncing switches, and setting pulse widths. The time delay is predictable based on τ.
Capacitors smooth out voltage ripple in power supplies. The RC time constant determines how effectively the ripple is filtered.
RC circuits block DC while passing AC signals (coupling), or filter high-frequency noise from power rails (decoupling).
At 5τ, the capacitor reaches 99.3% of full charge - close enough to 100% for most practical purposes. The charging curve is exponential, so it theoretically never reaches exactly 100%.
A larger resistor increases τ, meaning the capacitor charges more slowly. This is useful for longer time delays but reduces the maximum charging current.
Yes! The same RC circuit becomes a high-pass filter if you take the output across the resistor instead of the capacitor. The cutoff frequency formula remains the same.
Both resistors and capacitors have temperature coefficients. For precision timing, use components with low temperature coefficients (metal film resistors, C0G/NP0 capacitors).