Calculate the RC time constant, capacitor voltage at any point during charging or discharging, time to reach a target voltage, and stored charge & energy.
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RC Circuit Formulas
All capacitor charging and discharging calculations derive from two fundamental equations:
Key Formulas
Time Constant
τ = R × C
Charging Voltage
V(t) = Vs × (1 − e^(−t/τ))
Discharging Voltage
V(t) = V₀ × e^(−t/τ)
Time to Voltage
t = −τ × ln(1 − Vt/Vs)
Stored Charge
Q = C × V
Stored Energy
E = ½ × C × V²
Worked Examples
1RC time constant
Resistance R10 kΩ
Capacitance C100 µF
τ = R × C1 s
Full charge (5τ)≈ 5 s
2Voltage after 500 ms
Supply Vs5 V
R = 10 kΩ, C = 100 µFτ = 1 s
V(0.5 s) = 5×(1−e⁻⁰·⁵)≈ 1.97 V
3Time to 3.15 V (63.2%)
Supply Vs5 V
Target Vt3.15 V
R = 10 kΩ, C = 100 µFτ = 1 s
t = −1 × ln(1−3.15/5)≈ 1 s (= 1τ)
4Energy stored
Capacitance C1000 µF
Voltage V12 V
Q = C × V12 mC
E = ½ × C × V²72 mJ
Frequently Asked Questions
What is the RC time constant? ▾
The RC time constant (τ = R × C) is the time it takes a capacitor to charge to 63.2% of the supply voltage through a resistor. After 5τ the capacitor is considered fully charged (99.3%). It also equals the discharge time to fall to 36.8% of the initial voltage.
How do I calculate capacitor voltage at time t? ▾
For charging: V(t) = Vs × (1 − e^(−t/RC)). For discharging: V(t) = V₀ × e^(−t/RC). Vs is the supply voltage, V₀ is the starting voltage, R is resistance in ohms, C in farads, and t in seconds.
How long does it take a capacitor to fully charge? ▾
A capacitor reaches 99.3% charge after 5 time constants (5τ). For example, R = 10 kΩ and C = 100 µF gives τ = 1 s, so full charge takes about 5 seconds.
How much energy is stored in a capacitor? ▾
Energy E = ½ × C × V². A 1000 µF capacitor charged to 12 V stores E = 0.5 × 0.001 × 144 = 72 mJ. The stored charge is Q = C × V = 0.001 × 12 = 12 mC.
Does higher capacitance mean slower charging? ▾
Yes. Since τ = R × C, doubling the capacitance doubles the time constant and makes charging twice as slow. Similarly, doubling the resistance also doubles τ. To charge faster, use a smaller resistor or smaller capacitor.