RC & RL Time Constant

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τ = RC and τ = L/R, the capacitor voltage at any time while charging or discharging, and the time to 63.2 % and practically full (5τ)

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Enter the values

What to work out

Resistance (R)

Capacitance (C)

Supply voltage (Vs)

Time (t)

Result

Time constant (τ)

Capacitor voltage at time t

7.585V

After 5τ the value is about 99.3 % of the way, so it is taken as practically complete.

Working

Formulas

Assumptions

Ideal parts: capacitor leakage and coil resistance ignored; for charging the capacitor starts empty, for RL the current starts at zero.
At 1τ charging reaches 1 − e⁻¹ ≈ 63.2 %; discharging leaves e⁻¹ ≈ 36.8 %.

Sources: Robert Boylestad, Introductory Circuit Analysis

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