RC Circuit Simulator
Simulate capacitor charging and discharging curves
RC Circuit Formulas
| Quantity | Formula | Meaning |
|---|
| Time constant | tau = R x C | Main timing value of the RC circuit. |
| Charging voltage | Vc(t) = Vs(1 - e^(-t/RC)) | Capacitor voltage while charging. |
| Discharging voltage | Vc(t) = V0e^(-t/RC) | Capacitor voltage while discharging. |
| Initial current | I0 = V / R | Current at the start of charging or discharging. |
Practical Rules
- After 1 tau, a charging capacitor reaches about 63.2% of the final voltage.
- After 3 tau, it reaches about 95% of the final voltage.
- After 5 tau, it is usually treated as nearly fully charged or discharged.
- Increasing resistance or capacitance makes the circuit respond more slowly.
Example: R = 10 kOhm and C = 100 uF gives tau = 1 second. During charging, Vc is about 63.2% of final voltage at t = tau.
Step-by-Step Charging Example
For R = 10 kOhm and C = 100 uF, convert the capacitor to farads: 100 uF = 0.0001 F. The time constant is tau = R x C = 10000 x 0.0001 = 1 s. With a 5 V supply, the charging voltage after 1 second is Vc = 5 x (1 - e^-1), which is about 3.16 V.
RC Timing Reference
| Time | Charging level | Discharging level |
|---|
| 1 tau | about 63.2% | about 36.8% |
| 2 tau | about 86.5% | about 13.5% |
| 3 tau | about 95.0% | about 5.0% |
| 5 tau | about 99.3% | about 0.7% |
Where RC Circuits Are Used
- Delay and timing circuits where a voltage changes gradually.
- Signal smoothing and simple low-pass or high-pass filters.
- Switch debouncing, reset circuits, and capacitor charge/discharge experiments.
Frequently Asked Questions
What is the RC time constant?▼
The time constant tau is R times C. After one tau, a charging capacitor reaches about 63.2% of the final voltage.
What is the charging formula?▼
For charging, capacitor voltage is Vc(t) = Vs * (1 - exp(-t/RC)).
What is the discharging formula?▼
For discharging, capacitor voltage is Vc(t) = V0 * exp(-t/RC).
Why simulate an RC circuit?▼
Simulation helps visualize delays, filters, timing circuits, and capacitor behavior over time.
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