Calculate τ = R × C and Charge/Discharge Percentages
Mode
Resistance R (Ω)
Capacitance C (F)
Target % (0-99.9)
Time t (s)
Result
Time Constant τ
Result
Step-by-Step Calculation
RC Time Constant Formulas
τ = R × C (seconds)
Charge: V(t) = V₀ × (1 - e^(-t/τ))
Discharge: V(t) = V₀ × e^(-t/τ)
Time to % charge: t = -τ × ln(1 - %/100)
The RC time constant defines the exponential charging and discharging speed of a capacitor through a resistor. One time constant (1τ) marks 63.2% completion. Practical steady state is reached after 5τ (99.3%). The formula applies to any first-order RC circuit.
⚠At t=0, capacitor acts like a short circuit (charging starts at max current). At t=5τ, current drops to near zero. For discharge, initial current is V₀/R.
Understanding the RC Time Constant
The time constant τ = RC is the fundamental parameter of any first-order RC circuit. It determines how fast the circuit responds to changes. A larger τ means slower response (longer to charge/discharge). Smaller τ means faster response. This applies to filters, timing circuits, and coupling networks.
Time Constant τ
τ = RC. 1τ = 63.2% charge. 2τ = 86.5%. 3τ = 95%. 5τ = 99.3%. Each τ multiplies by e.
Exponential Nature
Fast initial change, slowing over time. The derivative (rate of change) = (V₀-V(t))/RC. Never truly zero, but negligible after 5τ.
Filter Cutoff
For RC filters: fc = 1/(2πRC). The cutoff frequency where output = 70.7% (-3dB) of input. τ and fc are inversely related.
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