FAQ
TL;DR: In an RC circuit, one time constant τ=RC brings a capacitor to 63% of its final voltage; “T=RC is the time it takes to achieve 63% of full charge.” [Elektroda, Steve Lawson, post #21662471]
Why it matters: These rules let you estimate charge/discharge timing, select parts, and avoid over‑voltage damage in real designs.
Quick Facts
- τ (tau) equals R×C; at 1τ the capacitor reaches about 63% of the applied DC voltage. [Elektroda, Steve Lawson, post #21662471]
- After 5τ, charge is about 99.3% complete; this is commonly treated as “near full.” [Elektroda, Steve Lawson, post #21662471]
- Cutoff frequency for a first‑order RC is fc = 1/(2πRC). [Elektroda, Steve Lawson, post #21662473]
- “Fully charged” means the capacitor voltage equals the applied source voltage. [Elektroda, Steve Lawson, post #21662481]
- Voltage rating (withstand) is a maximum safe voltage; it does not change τ or charge speed. [Elektroda, Steve Lawson, post #21662479]
What does the time constant T=RC actually mean?
The time constant τ=RC is the characteristic time of a first‑order RC circuit. After one τ, the capacitor’s voltage has moved 63% of the way from its start value toward the final value set by the source. After two τ it’s about 86.5%. After five τ it’s roughly 99.3%. These percentages apply to charging and discharging. “It’s the same thing in reverse for a capacitor discharging.” [Elektroda, Steve Lawson, post #21662471]
When is a capacitor considered fully charged?
Fully charged means the capacitor’s terminal voltage equals the applied source voltage. The RC curve approaches this level asymptotically, so engineers treat about five time constants as effectively full for design timing. “Fully charged means, charged to the same voltage as the applied voltage.” [Elektroda, Steve Lawson, post #21662481]
How do I calculate capacitor voltage vs. time during charging?
Use vc(t) = vin·(1 − e^(−t/RC)) if the initial voltage is zero. For a non‑zero initial voltage vc(0), use vc(t) = [vc(0) − vin]·e^(−t/RC) + vin. These equations let you read the capacitor’s voltage at any moment and see how it approaches vin as t increases. [Elektroda, ASAD ALI, post #21662470]
How many time constants does it take to reach near full charge?
About five. At 1τ the capacitor is ~63% toward final; 2τ ≈ 86.5%; 3τ ≈ 95%; 4τ ≈ 98%; 5τ ≈ 99.3%. Designers commonly call 5τ “fully charged” for practical timing. This rule of thumb speeds estimates without full simulation. [Elektroda, Steve Lawson, post #21662471]
Does the capacitor’s voltage rating affect how fast it charges?
No. The printed voltage rating (withstand) is only the maximum safe operating voltage. It does not influence τ or the charge/discharge rate. Time behavior depends only on R and C. Change R or C to change timing; keep the applied voltage below the rating to avoid damage. [Elektroda, Steve Lawson, post #21662479]
What happens if I exceed the capacitor’s voltage rating?
Exceeding the withstand voltage risks dielectric breakdown and failure. The insulation between plates can be damaged, leading to leakage or a short. “If the terminal voltage exceeds the withstand voltage, then the capacitor will probably fail.” Always choose a rating with margin over the highest expected voltage. [Elektroda, Steve Lawson, post #21662481]
How does RC relate to cutoff frequency?
A first‑order RC has cutoff frequency fc = 1/(2πRC). Equivalently, τ = RC = 1/(2πfc). This ties time‑domain behavior (τ) to frequency‑domain behavior (−3 dB point) for the same network. It’s useful when swapping between timing specs and filter specs. [Elektroda, Steve Lawson, post #21662473]
Is the RC time constant the total time to charge a capacitor?
No. The time constant is one segment of the process, not the whole time. The capacitor asymptotically approaches its final voltage. Engineers often use 5τ as the practical endpoint. “The time constant is one segment of the time needed to charge or discharge.” [Elektroda, Steve Lawson, post #21662487]
How does discharging follow the time constant?
Discharge mirrors charge behavior. After one τ, the voltage has dropped by 63%, leaving 37% of the initial value. After five τ, about 0.7% remains. This symmetry lets you reuse the same exponential equation with a negative sign for the change. “It’s the same thing in reverse for a capacitor discharging.” [Elektroda, Steve Lawson, post #21662471]
Quick how‑to: estimate RC charge time without math?
- Compute τ = R×C from your resistor (Ω) and capacitor (F).
- Multiply τ by 5 for near‑full charge (~99.3%).
- For checkpoints, use 1τ≈63%, 2τ≈86.5%, 3τ≈95%.
These milestones provide fast design estimates for microcontroller delays or analog settling. [Elektroda, Steve Lawson, post #21662471]
Why does the charging current slow down over time?
As the capacitor’s voltage rises, the voltage difference across the resistor shrinks, reducing current exponentially. A good analogy is a water tank draining through a small hole: fast at first, then slower as the level drops. This maps to the same exponential behavior in RC circuits. [Elektroda, Earl Albin, post #21662475]
Can an RC capacitor charge above the source voltage with DC?
No. In a simple RC with a DC source, the capacitor’s final voltage equals the applied source voltage. It cannot exceed that level without additional circuitry like charge pumps or inductive kickback paths. “Fully charged means… the same voltage as the applied voltage.” [Elektroda, Steve Lawson, post #21662481]
Does changing the source voltage change the time constant?
No. Time constant depends only on R and C. Changing the source voltage changes the final target voltage, not the speed of approach. “Regardless the charging voltage, the value of the resistor and the capacitor determine the time it takes.” [Elektroda, Steve Lawson, post #21662476]
