RC time constant calculator

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Result

Time constant τ470 ms

Capacitor voltage5.662 V

Charged47.18 %

Practically full (5τ)2350 ms

Step-by-step solution

Time constant

τ = R·C = 10 kΩ · 47 µF = 470 ms

Charging an empty capacitor

v_C(t) = V_s·(1 − e^−t/τ)

v_C = 12·(1 − e^−300/470) = 5.662 V

Key formulas

Time constant: τ = RC | τ = L/R
Response: x(t) = x(∞) + [x(0) − x(∞)]·e^−t/τ
Capacitor at DC: open circuit; v_C cannot jump
Inductor at DC: short circuit; i_L cannot jump
Settled: t ≈ 5τ

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