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RC Circuit Time Constant Calculator

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Charge / Discharge Table

وقت	Multiple	% of Final	Charging	Discharging
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RC Circuit Time Constant Calculator

The RC Circuit Time Constant Calculator computes τ = R × C for resistor-capacitor circuits and τ = L / R for resistor-inductor circuits, with automatic SI unit conversion. It generates a charge / discharge table at one through five time constants and tells you how long the circuit needs to reach a target percentage of its final value, so you can size timing components without paper math or guesswork.

كيفية استخدام

Pick the circuit type — RC (resistor + capacitor) or RL (resistor + inductor).
Enter the resistance and choose the matching unit (mΩ, Ω, kΩ, MΩ).
Enter the capacitance (pF / nF / µF / mF / F) for RC, or the inductance (µH / mH / H) for RL.
Set the supply voltage Vs to scale the charge and discharge values.
Optionally enter a target percentage to see the time required to reach that level of the final value.
Read the time constant, the 1τ – 5τ table, and the target-time result.

خصائص

RC and RL modes – computes τ = R × C for capacitive circuits and τ = L / R for inductive circuits.
Auto unit conversion – picks pF→F, kΩ→Ω, µH→H and reformats results in human-readable prefixes (ns, µs, ms, s).
Charge / discharge table – voltage or current at 1τ, 2τ, 3τ, 4τ, 5τ with the standard 63.2%, 86.5%, 95.0%, 98.2%, 99.3% milestones.
Custom target time – solves t = −τ × ln(1 − fraction) for any target percentage you enter.
Steady-state hint – shows I_max = Vs / R for RL or Vs for RC so you know the curve’s asymptote.
تحديثات حية – the result, table, and target time recompute as you type or change units.

 التعليمات

What is the time constant in an RC circuit?

The time constant τ (tau) of an RC circuit equals the resistance multiplied by the capacitance, τ = R × C. It has units of seconds and measures how quickly the capacitor charges or discharges through the resistor. After one time constant, a charging capacitor has reached about 63.2% of the supply voltage; after five time constants, it is considered fully charged (≈ 99.3%).
How is the RL time constant different from the RC time constant?

For a resistor-inductor circuit the time constant is τ = L / R, not R × C. Instead of describing how voltage builds on a capacitor, it describes how current builds (or decays) through an inductor. The same exponential form applies: i(t) = I_max × (1 − e^(−t/τ)) when energising, and i(t) = I_0 × e^(−t/τ) when de-energising.
Why does an RC circuit reach 63.2% after one time constant?

The charging equation V(t) = Vs × (1 − e^(−t/τ)) becomes V(τ) = Vs × (1 − 1/e). The value 1 − 1/e ≈ 0.6321, so after one τ the capacitor has reached about 63.2% of the supply voltage. The number is intrinsic to the exponential decay of the curve, not to any particular component.
How long does it take a capacitor to fully charge?

Mathematically, a capacitor never fully reaches the supply voltage — the exponential curve only approaches it. Engineers use the convention that the capacitor is fully charged after about 5τ, by which point the voltage is about 99.3% of Vs. Beyond 5τ the remaining error is typically below circuit tolerance.
Why do unit prefixes matter in RC calculations?

Component values can span twelve orders of magnitude: capacitors in picofarads (10⁻¹²) up to farads, resistors from milliohms to megaohms. The product R × C lands anywhere from nanoseconds to hours, so converting every value to SI base units (ohms and farads) before multiplying is the only way to get a correct result, especially when the inputs are in different scales like kΩ and µF.