# 电容充放电 - Capacitor Charge/Discharge

展示RC电路电容充放电过程中电压、电流和电荷积累的交互式模拟

> 标准页面: https://elysiatools.com/zh/visualizations/capacitor-charge-discharge

- **分类:** Physics

## 概述

Interactive RC circuit simulation demonstrating capacitor charging and discharging with exponential voltage/current curves, time constant visualization, and circuit animation. Features charging equation: q(t) = Q₀(1 - e^(-t/RC)), discharging equation: q(t) = Q₀·e^(-t/RC), time constant: τ = RC, voltage: V = q/C, charging current: I = (V₀/R)·e^(-t/RC), discharging current: I = -(Q₀/RC)·e^(-t/RC). Real-time visualization includes: (1) Circuit diagram with animated switch connecting battery (charge) or short circuit (discharge), resistor, and capacitor; (2) Electron flow animation showing current direction and magnitude; (3) Charge accumulation animation with positive (red) and negative (blue) charges on capacitor plates; (4) Real-time voltage meter displaying capacitor voltage; (5) Charge/discharge curves showing q(t) exponential behavior with theoretical curves overlay; (6) Split-screen comparison view showing charging vs discharging side by side; (7) Current curve I(t) showing positive (charge) and negative (discharge) exponential decay. Adjustable parameters: resistance R (10-1000 kΩ), capacitance C (1-100 μF), source voltage V₀ (1-50 V), animation speed (0.1-3.0x), time window (5-30 s), particle animation speed (0.5-2.0x), and curve opacity (0.3-1.0). Display options: show/hide electron flow, charge accumulation, voltage meter. Time constant markers show τ, 2τ, 3τ, 4τ, 5τ positions on curves (63.2%, 86.5%, 95.0%, 98.2%, 99.3% charged/discharged). Educational content covers exponential charging/discharging process, RC time constant significance, energy storage: E = ½CV² = q²/(2C), practical applications: timing circuits, filters, power supply smoothing, camera flash units, defibrillators, energy storage in regenerative braking, touchscreens, coupling/decoupling in amplifiers, and memory elements. Multi-language support (zh, en, de, fr, es, ru, pt).

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