Capacitor Energy, Charge & Time Constant Calculator
Calculate energy stored in a capacitor, charge, voltage relationships, and RC circuit charging/discharging time constants.
Capacitors Guide
Capacitor Fundamentals
A capacitor stores energy in an electric field between two conducting plates. Capacitance C = Q/V (charge per unit voltage). Units: farads (F). Common values: microfarads (μF = 10⁻⁶ F), nanofarads (nF = 10⁻⁹ F), picofarads (pF = 10⁻¹² F). Energy stored: E = ½CV² = Q²/(2C) = ½QV. A 100μF capacitor charged to 12V: E = ½ × 100×10⁻⁶ × 144 = 0.0072 J = 7.2 mJ. A 1F supercapacitor at 2.7V: E = ½ × 1 × 7.29 = 3.6 J. Capacitors release their stored charge very rapidly — unlike batteries, they can delive
RC Circuits and Time Constant
When a capacitor charges through a resistor: V(t) = V_supply × (1 − e^(−t/τ)). When discharging: V(t) = V₀ × e^(−t/τ). Where τ = RC (time constant in seconds). At t = τ: charging: V = 63.2% of supply. Discharging: V = 36.8% of V₀. At 5τ: 99.3% charged or 0.7% remaining — considered 'fully charged' or 'fully discharged'. Example: 10kΩ resistor × 100μF capacitor: τ = 10,000 × 100×10⁻⁶ = 1 second. Fully charged in approximately 5 seconds.
Capacitors in Series and Parallel
Parallel: 1/C_total = 1/C₁ + 1/C₂ + ... → total capacitance decreases. Series: C_total = C₁ + C₂ + ... → total capacitance increases. This is opposite to resistors. Parallel combination: same voltage across each capacitor, total charge adds. Useful for increasing capacitance. Series combination: same charge on each capacitor, total voltage adds. Useful for higher voltage ratings. Working voltage rating: if capacitor max voltage is 16V, connecting two in series enables 32V operation (each sees ha
Applications
Power supply smoothing: large electrolytic capacitors (1000μF+) smooth the pulsed DC from a rectifier, reducing ripple voltage. Flash photography: capacitor charged over seconds, discharged in microseconds through the flash tube — delivers enormous instantaneous power. Timing circuits: RC time constant controls timing in 555 timer circuits, oscillators, and filters. Energy storage: supercapacitors (farads to kilofarads) bridge the gap between capacitors and batteries — used in regenerative braki
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