RC Circuit Time Constant Calculator
Calculate RC time constant, charging voltage at any time and cut-off frequency.
Step-by-step working
- τ = R C = 10000 × 1.0000e-4 = 1 s
- V(t) = V₀(1 − e^(−t/τ)) = 5(1 − e^(−1/1))
| Time | Vc (V) | % of V₀ |
|---|---|---|
| 0τ = 0 s | 0 | 0% |
| 1τ = 1 s | 3.1606 | 63.21% |
| 2τ = 2 s | 4.3233 | 86.47% |
| 3τ = 3 s | 4.7511 | 95.02% |
| 4τ = 4 s | 4.9084 | 98.17% |
| 5τ = 5 s | 4.9663 | 99.33% |
Mathematical Formula
Overview & Explanation
A capacitor charges exponentially through a resistor with time constant τ.
How It Works
- τ = RC.
- Evaluate the exponential at t.
- Table shows 0–5τ.
Practical Applications
- Timers and delays.
- RC filter design.
Example 1: 10 kΩ, 100 μF, 5 V at 1 s
τ = 1 s.
Inputs
Resistance (Ω): 10000 · Capacitance (μF): 100 · Supply voltage (V): 5 · Time t (s): 1
Step 1
τ = R C = 10000 × 1.0000e-4 = 1 s
Step 2
V(t) = V₀(1 − e^(−t/τ)) = 5(1 − e^(−1/1))
Time constant τ
Result
Example 2: 1 kΩ, 1 μF filter
f_c ≈ 159 Hz.
Inputs
Resistance (Ω): 1000 · Capacitance (μF): 1 · Supply voltage (V): 3.3 · Time t (s): 0.002
Step 1
τ = R C = 1000 × 1.0000e-6 = 0.001 s
Step 2
V(t) = V₀(1 − e^(−t/τ)) = 3.3(1 − e^(−0.002/0.001))
Time constant τ
Result
How it's calculated & sources
τ = RC; V(t) = V₀(1 − e^(−t/τ)); f_c = 1/(2πRC).
Frequently Asked Questions
When is it fully charged?
Discharging?
Filter cut-off?
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