Components · #5 of 20
Capacitors + RC Time Constant
Charging, Filtering, Timing
Why it matters
Capacitors store energy, filter noise, and create time delays. The RC time constant (τ = R × C) tells you how fast they charge/discharge.
The idea
What Is a Capacitor?
A capacitor stores electrical energy in an electric field. Think of it as a tiny rechargeable battery \ that charges/discharges very quickly. <div class=Demo
Adjust Resistance and Capacitance to see how the charging curve changes.
Watch for:
- Time constant (τ) — how long until 63% charge
- Charging curve — exponential rise
- Effect of R and C — larger values = slower charging
Key takeaways
- Capacitors store energy in an electric field
- RC time constant: τ = R × C
- After 1τ: ~63% charged, after 5τ: ~99% charged
- Capacitors filter noise, create delays, and smooth power supplies
Going deeper
Capacitors have ESR (Equivalent Series Resistance) and leakage current. For power supply filtering, use ceramic capacitors (low ESR, good for high frequencies) and electrolytic capacitors (high capacitance, good for low frequencies). For timing, use film or ceramic capacitors (stable, low leakage).
Math details
RC charging equation:
V(t) = V_final × (1 - e^(-t/τ))
Where:
τ = R × C (time constant in seconds)
t = time
V_final = final voltage
At t = τ:
V(τ) = V_final × (1 - e^(-1)) ≈ V_final × 0.632
At t = 5τ:
V(5τ) = V_final × (1 - e^(-5)) ≈ V_final × 0.993
Example:
R = 10kΩ = 10,000Ω
C = 100µF = 0.0001F
τ = 10,000 × 0.0001 = 1 second
After 1 second: ~63% charged
After 5 seconds: ~99% charged