RC Circuit Capacitor Charge and Discharge: Time Constants Explained
RC circuits are fundamental building blocks in electronics, used for timing, filtering, and signal shaping. Learn how capacitors charge and discharge through a resistor, what the time constant is, and how to calculate RC values for your circuits.
The RC Circuit
An RC circuit consists of a resistor (R) and a capacitor (C) in series. It is one of the most fundamental circuits in electronics, used in:
- Timing circuits (555 timer configs)
- Low-pass and high-pass filters
- Debounce circuits for buttons
- Power supply smoothing
- Coupling and decoupling (DC blocking)
The Time Constant (τ)
The most important parameter of an RC circuit is the time constant τ (Greek letter tau):
τ = R × C
Where:
- R is in ohms (Ω)
- C is in farads (F)
- τ is in seconds (s)
The time constant defines how quickly the capacitor charges or discharges. After one time constant, the capacitor has reached approximately 63.2% of its final value when charging, or discharged to 36.8% when discharging.
Charging Equation
When charging through a resistor from 0V to Vs:
Vc(t) = Vs × (1 - e^(-t/τ))
| Time | Voltage (% of Vs) |
|---|---|
| 1τ | 63.2% |
| 2τ | 86.5% |
| 3τ | 95.0% |
| 4τ | 98.2% |
| 5τ | 99.3% |
A capacitor is considered fully charged after 5τ (99.3%).
Discharge Equation
When discharging through a resistor from an initial voltage V0:
Vc(t) = V0 × e^(-t/τ)
| Time | Voltage (% of V0) |
|---|---|
| 1τ | 36.8% |
| 2τ | 13.5% |
| 3τ | 5.0% |
| 4τ | 1.8% |
| 5τ | 0.7% |
Worked Examples
Example 1: Calculate τ for a timing circuit
R = 10kΩ, C = 100μF
τ = 10,000 × 0.0001 = 1 second
The capacitor charges to 63.2% of the supply voltage in 1 second and is fully charged in about 5 seconds.
Example 2: Design an RC delay for 200ms
We want the capacitor voltage to reach 63.2% of supply (one time constant) in 200ms, so τ = 0.200 s.
If we choose C = 10μF:
R = τ / C = 0.200 / 0.00001 = 20,000 Ω = 20 kΩ
Nearest standard value: 22kΩ (gives τ = 220ms).
Example 3: Button debounce
A pushbutton bounces (rapid make/break) for about 20ms. We want the RC circuit to filter bounces shorter than 50ms.
Using C = 100nF:
R = 0.050 / 0.0000001 = 500,000 Ω = 500 kΩ
Nearest standard value: 470kΩ.
RC as a Low-Pass Filter
An RC network also acts as a low-pass filter — it passes low-frequency signals but attenuates high-frequency ones. The -3dB cutoff frequency is:
fc = 1 / (2πRC) = 1 / (2πτ)
Signals below fc pass through (almost) unchanged; signals above fc are attenuated. At exactly fc, the signal is reduced to 70.7% of its original amplitude (-3dB).
This is used to remove high-frequency noise from sensor readings (place the RC filter at the ADC input) and to band-limit audio signals.
Capacitor Types and Polarity
For RC timing circuits, common capacitor types:
| Type | Polar? | Range | Notes |
|---|---|---|---|
| Electrolytic | Yes | 1μF–10,000μF | Must observe polarity; leaky at low values |
| Tantalum | Yes | 0.1μF–1,000μF | Better than electrolytic; still observe polarity |
| Ceramic (MLCC) | No | 1pF–100μF | Preferred for small values and filters |
| Film | No | 1nF–100μF | Most stable; used in precision timing |
Electrolytic and tantalum capacitors are polarised — connect incorrectly and they can fail explosively. The negative terminal (cathode) is marked with a stripe; in circuit diagrams, the curved plate of the capacitor symbol is the negative terminal.