RC Circuit Charge Time Calculator

When a capacitor charges through a resistor, the voltage across the capacitor rises exponentially toward the source voltage. It never reaches the source voltage instantaneously; instead it follows:

V(t) = V₀ × (1 − e^(−t/RC))

where τ = RC is the time constant — the fundamental timing parameter of the circuit.

What is the time constant τ = RC?

The time constant τ (tau) is the time it takes the capacitor to charge to about 63.2% of the source voltage. It depends on:

• Resistance R in ohms (Ω): more resistance = slower charging
• Capacitance C in farads (F): more capacitance = slower charging

Charging milestones:

Why does this matter?

RC time constants are everywhere in electronics:

• Camera flash circuits charge a capacitor through a resistor
• Audio tone controls use RC networks to boost or cut frequencies
• Digital circuits use RC delays to debounce switches and set timing
• Power supplies use large RC time constants for smooth filtering

Example: An RC circuit with R = 10 kΩ and C = 100 μF has τ = 10,000 × 0.0001 = 1 second. It takes about 5 seconds to fully charge a capacitor from 0 V to nearly the supply voltage.

Charge and energy at the end

Once the capacitor settles at the source voltage, it holds:

• Charge: Q = C × V (coulombs)
• Energy: E = ½ × C × V² (joules)

A 100 μF cap at 12 V settles with Q = 1.2 mC of charge and E = 7.2 mJ of stored energy. Energy scales with V², so a 300 V camera-flash cap at the same 100 μF stores ~4.5 J, 625 times more energy at 25× the voltage.

Common capacitance values in the wild

• Bypass / decoupling: 100 nF (0.1 μF) ceramic, right next to every digital chip
• Power supply filter: 470 μF to 10,000 μF aluminum electrolytic
• Audio coupling: 1 to 100 μF film or electrolytic
• Camera flash: 100 to 1000 μF rated for 300 V (stores 4.5 to 45 J)
• Supercapacitors: 1 to 3000 F at low voltage, used for short-duration energy storage and EV regenerative braking

Safety note

Large capacitors hold dangerous charge long after power is removed. The 10,000 μF filter cap in a tube amplifier or microwave oven can deliver a lethal shock days after the unit is unplugged. Always discharge through a bleeder resistor before working on circuits with caps over a few μF rated above 50 V.