時定数 計算ツール
RC/RL過渡応答
Required Parameters
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Quick Answer
The time constant (τ) determines how fast an RC or RL circuit responds to a step change. RC: τ = R×C. RL: τ = L/R. After 5τ, the circuit has settled to 99.3% of its final value.
時定数 計算ツール
充放電回路の RC / RL 時定数（τ） を計算します。時定数は、コンデンサの充電やインダクタの電流立ち上がりがどれだけ速いかを決めます。
RC 時定数
τ = R × C
1τ 経過後、コンデンサは最終電圧の 63.2% に達します。5τ 後はほぼ充電完了（99.3%）とみなします。
| 時間 | 充電率 | 残り |
|---|---|---|
| 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% |
RL 時定数
τ = L / R
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Design Notes
The time constant connects two fundamental domains: time response and frequency response. A circuit with τ = 1ms has a bandwidth of fc = 1/(2πτ) = 159 Hz. This means slower circuits (larger τ) filter more noise but respond more sluggishly to input changes. In digital design, minimizing parasitic RC (stray capacitance × trace resistance) is critical for achieving fast rise times: t_rise ≈ 2.2τ.
Common Mistakes
- 1
Forgetting that RL and RC time constants have opposite dependencies on R — increasing R makes RC slower but RL faster.
- 2
Assuming the circuit reaches final value after one time constant. One τ only reaches 63.2% — you need 5τ for practical completion.
- 3
Not accounting for source impedance when calculating the time constant of an RC network driven by a non-ideal source.
Engineering Handbox
1. τ = R × C = 10,000 × 47 × 10⁻⁶ = 0.47 seconds 2. Time to 95%: 3τ = 1.41 seconds 3. Time to 99.3%: 5τ = 2.35 seconds 4. Cutoff frequency: fc = 1/(2π × 0.47) = 0.339 Hz
Knowledge Base
時定数（τ）とは？
RC/RL回路が最終値の63.2%に達する時間。RC: τ = R×C、RL: τ = L/R。
完全充電まで何τ必要？
1τ=63.2%、2τ=86.5%、3τ=95%、5τ=99.3%。5τで実用上「完全」とみなします。
充電時の電圧方程式は？
V(t) = V最終 × (1 - e^(-t/τ))（充電）、V(t) = V初期 × e^(-t/τ)（放電）。
カットオフ周波数との関係は？
fc = 1/(2πτ)。時定数が長いほどカットオフ周波数は低くなります。
チャタリング防止での重要性は？
機械スイッチは1〜10msバウンスします。τ=5〜10ms（例：10kΩ+1µF）でチャタリングを除去。
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