Calculate charging/discharging time and voltage for RC circuits.
V(t) = Vs × (1 - e-t/RC)
When charging from 0V, the capacitor voltage rises exponentially toward the supply voltage. After one time constant (τ = RC), it reaches ~63.2% of the supply voltage.
V(t) = V0 × e-t/RC
When discharging, the voltage decreases exponentially. After one time constant, it drops to ~36.8% of the initial voltage.
| Time Constants (τ) | 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% |
A capacitor is considered fully charged/discharged after 5τ (99.3%)
Create delayed startup circuits. A 10kΩ resistor with 100µF capacitor gives τ = 1 second delay to reach 63% of supply voltage.
RC circuits filter mechanical switch bounce. Typical values: 10kΩ and 100nF for τ = 1ms debounce time.
AC coupling capacitors block DC while passing audio. Lower τ = higher cutoff frequency. fc = 1/(2πRC).
Convert PWM to analog voltage. τ should be much larger than PWM period for smooth output with minimal ripple.
555 timers and monostable circuits use RC charging to set pulse width and oscillation frequency.
Capacitors store analog voltages. Larger capacitor and higher input impedance = longer hold time with less droop.
Real capacitors have Equivalent Series Resistance (ESR) that adds to the circuit resistance, affecting actual charge times.
Electrolytic capacitors have significant leakage, causing them to discharge slowly even without a load.
Capacitance varies with temperature. Ceramic capacitors especially can lose significant capacitance at temperature extremes.
The voltage source's internal resistance adds to R in the RC time constant. For accurate timing, use low-impedance sources.