Capacitor Charge/Discharge Calculator
Analyze RC charging and discharging. Calculate time constant, voltage at any time, current, charge, and stored energy. Live exponential curve visualization with τ, 2τ, 5τ markers.
How to Use
- Choose Charging (cap starts at 0V) or Discharging (cap starts at Vs).
- Enter supply voltage, resistance, and capacitance.
- Enter a time t to see the voltage and current at that instant.
- The curve shows the exponential with key percentages (63%, 86%, 95%, 99%).
- Use suffix notation: 10k, 4.7M, 100nF, 22uF, 10ms, 5us.
Show Work
Formulas
Percentages vs. Time
| Time | Charging % | Discharging % |
|---|---|---|
| 1 τ | 63.21% | 36.79% |
| 2 τ | 86.47% | 13.53% |
| 3 τ | 95.02% | 4.98% |
| 4 τ | 98.17% | 1.83% |
| 5 τ | 99.33% | 0.67% |
| 7 τ | 99.91% | 0.09% |
History of the RC Circuit
The capacitor itself dates to the Leyden jar of 1745, independently discovered by Ewald Georg von Kleist and Pieter van Musschenbroek at the University of Leiden — a glass bottle coated inside and out with metal foil, capable of storing static charge from a friction machine. Benjamin Franklin coined the term "battery" for arrays of them and showed that the charge lived on the glass dielectric, not the foil. The word "capacitance" came much later, as 19th-century physicists formalized what the Leyden jar did.
The differential equation that governs RC charging — dV/dt proportional to the remaining gap — was worked out by the generation of mathematical physicists following Michael Faraday. Faraday himself defined the farad as the unit of capacitance in the 1830s (though the first capacitors with farad-scale values wouldn't exist for a century). By the time Oliver Heaviside and George Campbell were designing the first loading coils and filters for long-distance telephony in the 1890s, the exponential response Vc(t) = Vs × (1 − e−t/τ) was a standard tool.
The same equation reappears everywhere in nature: Newton's law of cooling, atmospheric pressure versus altitude, radioactive decay, drug metabolism, capital investment with fixed returns. Master the RC response once and you understand the dynamics of a huge class of physical systems — which is why it's the first differential equation most engineering students solve.
About This Calculator
Pick Charging (capacitor starts at 0 V) or Discharging (capacitor starts at Vs), enter R and C with standard engineering suffixes, and optionally enter a time t to see the voltage and current at that instant. The live curve plots the full exponential with τ, 2τ, 3τ, 4τ, and 5τ markers so you can see exactly where your t lands.
Current starts at Vs/R (cap fully empty, all voltage across R) and decays to zero as charging completes. Stored energy is ½·C·Vc². Big electrolytic caps in tube amps and power supplies store enough energy to be dangerous — always discharge a reservoir cap through a bleeder before servicing. All math runs client-side; no values leave your browser.
Frequently Asked Questions
What is the RC time constant?
τ = R × C. It's the time the capacitor takes to reach 63.2% of its final voltage when charging, or drop to 36.8% of initial when discharging. After 5τ the cap is within 1% of its steady-state value — often considered "fully charged."
How long until it's "fully charged"?
Strictly, never — an RC circuit approaches final voltage asymptotically. Practically: 1τ = 63%, 2τ = 86%, 3τ = 95%, 4τ = 98%, 5τ = 99.3%. Most engineers use 5τ as the rule of thumb for "fully charged."
How much energy is stored?
E = ½ × C × V². That 10µF cap at 12V stores 0.72 mJ. Big electrolytic caps in power supplies store significant energy — always discharge before service. A 470µF cap at 400V stores 37.6 J, enough for a painful shock.
Why does current start high and decrease?
At t=0, the capacitor has no voltage, so the full Vs appears across R — peak current = Vs/R. As the cap charges, its voltage opposes Vs, reducing the voltage across R and therefore the current. Current follows the same exponential as charging voltage (inverted).
What's the difference between charging and discharging?
Mathematically mirror images. Charging: Vc(t) = Vs × (1 − e^(−t/τ)). Discharging: Vc(t) = V0 × e^(−t/τ). Charging curve starts at 0 and approaches Vs; discharging starts at V0 and approaches 0. Same τ in both cases.
How does leakage affect this?
Real capacitors have internal leakage resistance (Rleak) in parallel with the ideal capacitance. For most ceramic and film caps, Rleak is in the hundreds of MΩ — negligible. Electrolytics leak more (tens of MΩ). Supercapacitors and high-value electrolytics self-discharge measurably over hours.
Common Use Cases
Power-On Delay
A slow RC charging an enable line — ensures the MCU starts only after rails have stabilized. Typical: R=100k, C=10µF → ~5s to 99%.
Debounce Capacitor
Parallel cap on a switch with a pullup forms an RC debouncer. Pick τ longer than the bounce (~1ms) but shorter than the response window.
Flash Capacitor Discharge
Camera flash: ~500µF at 350V stores 30J. Dumps through xenon tube in microseconds — very high peak current and bright flash.
AC-to-DC Smoothing
Rectifier output ripple is smoothed by a reservoir cap. Sizing: C ≥ I_load × T_cycle / V_ripple. RC τ sets the ripple profile.
Analog Sample-and-Hold
ADC input cap needs time to charge through the source impedance. Conversion error < 0.1 LSB requires charging for ~7τ.
Safety Discharge Resistor
Bleeder across a power supply reservoir cap. Sized for slow bleed when unpowered (5 min ~ 5τ) but negligible steady-state loss.
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